• create a dump of 10.5 or earlier including mysql schema etc. A dump of all databases from a freshly bootstrapped server will do (10.5.dump)
• shut down 10.5, bootstrap and start a fresh 10.6+
• load the dump of 10.5 into 10.6
• run mysql_upgrade (it will likely require --force)
• see the output

  10.6 70021737
  Phase 1/7: Checking and upgrading mysql database
  Processing databases
  mysql
  mysql.column_stats OK
  mysql.columns_priv OK
  mysql.db OK
  mysql.event OK
  mysql.func OK
  mysql.global_priv OK
  mysql.gtid_slave_pos OK
  mysql.help_category OK
  mysql.help_keyword OK
  mysql.help_relation OK
  mysql.help_topic OK
  mysql.index_stats OK
  mysql.innodb_index_stats OK
  mysql.innodb_table_stats OK
  mysql.plugin OK
  mysql.proc OK
  mysql.procs_priv OK
  mysql.proxies_priv OK
  mysql.roles_mapping OK
  mysql.servers OK
  mysql.table_stats OK
  mysql.tables_priv OK
  mysql.time_zone OK
  mysql.time_zone_leap_second OK
  mysql.time_zone_name OK
  mysql.time_zone_transition OK
  mysql.time_zone_transition_type OK
  mysql.transaction_registry OK
  Phase 2/7: Installing used storage engines... Skipped
  Phase 3/7: Fixing views
  mysql.user OK
  sys.host_summary
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.host_summary_by_file_io
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.host_summary_by_file_io_type
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.host_summary_by_stages
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.host_summary_by_statement_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.host_summary_by_statement_type
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.innodb_buffer_stats_by_schema
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.innodb_buffer_stats_by_table
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.innodb_lock_waits
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.io_by_thread_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.io_global_by_file_by_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.io_global_by_file_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.io_global_by_wait_by_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.io_global_by_wait_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.latest_file_io
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.memory_by_host_by_current_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.memory_by_thread_by_current_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.memory_by_user_by_current_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.memory_global_by_current_bytes
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.memory_global_total
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.metrics OK
  sys.processlist
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.ps_check_lost_instrumentation OK
  sys.schema_auto_increment_columns OK
  sys.schema_index_statistics
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.schema_object_overview OK
  sys.schema_redundant_indexes OK
  sys.schema_table_lock_waits
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.schema_table_statistics
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.schema_table_statistics_with_buffer
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.schema_tables_with_full_table_scans
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.schema_unused_indexes OK
  sys.session
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.session_ssl_status OK
  sys.statement_analysis
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.statements_with_errors_or_warnings
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.statements_with_full_table_scans
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.statements_with_runtimes_in_95th_percentile
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.statements_with_sorting
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.statements_with_temp_tables
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary_by_file_io
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary_by_file_io_type
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary_by_stages
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary_by_statement_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.user_summary_by_statement_type
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.version OK
  sys.wait_classes_global_by_avg_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.wait_classes_global_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.waits_by_host_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.waits_by_user_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.waits_global_by_latency
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.x$host_summary OK
  sys.x$host_summary_by_file_io OK
  sys.x$host_summary_by_file_io_type OK
  sys.x$host_summary_by_stages OK
  sys.x$host_summary_by_statement_latency OK
  sys.x$host_summary_by_statement_type OK
  sys.x$innodb_buffer_stats_by_schema OK
  sys.x$innodb_buffer_stats_by_table OK
  sys.x$innodb_lock_waits OK
  sys.x$io_by_thread_by_latency OK
  sys.x$io_global_by_file_by_bytes OK
  sys.x$io_global_by_file_by_latency OK
  sys.x$io_global_by_wait_by_bytes OK
  sys.x$io_global_by_wait_by_latency OK
  sys.x$latest_file_io OK
  sys.x$memory_by_host_by_current_bytes OK
  sys.x$memory_by_thread_by_current_bytes OK
  sys.x$memory_by_user_by_current_bytes OK
  sys.x$memory_global_by_current_bytes OK
  sys.x$memory_global_total OK
  sys.x$processlist OK
  sys.x$ps_digest_95th_percentile_by_avg_us OK
  sys.x$ps_digest_avg_latency_distribution OK
  sys.x$ps_schema_table_statistics_io
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.x$schema_flattened_keys OK
  sys.x$schema_index_statistics OK
  sys.x$schema_table_lock_waits
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.x$schema_table_statistics
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.x$schema_table_statistics_with_buffer
  Error : Cannot load from mysql.proc. The table is probably corrupted
  error : Corrupt
  sys.x$schema_tables_with_full_table_scans OK
  sys.x$session OK
  sys.x$statement_analysis OK
  sys.x$statements_with_errors_or_warnings OK
  sys.x$statements_with_full_table_scans OK
  sys.x$statements_with_runtimes_in_95th_percentile OK
  sys.x$statements_with_sorting OK
  sys.x$statements_with_temp_tables OK
  sys.x$user_summary OK
  sys.x$user_summary_by_file_io OK
  sys.x$user_summary_by_file_io_type OK
  sys.x$user_summary_by_stages OK
  sys.x$user_summary_by_statement_latency OK
  sys.x$user_summary_by_statement_type OK
  sys.x$wait_classes_global_by_avg_latency OK
  sys.x$wait_classes_global_by_latency OK
  sys.x$waits_by_host_by_latency OK
  sys.x$waits_by_user_by_latency OK
  sys.x$waits_global_by_latency OK
  Phase 4/7: Running 'mysql_fix_privilege_tables'
  Phase 5/7: Fixing table and database names
  Phase 6/7: Checking and upgrading tables
  Processing databases
  information_schema
  performance_schema
  sys
  sys.sys_config OK
  test
  tmp
  Phase 7/7: Running 'FLUSH PRIVILEGES'
  OK

The problem here, as far as I can tell, is that first it tries to check views, including sys schema, which survived the dump load because it doesn't exist in 10.5, but its functions cannot be loaded because mysql.proc structure has changed. mysql.proc is upgraded later, and later sys views are even re-created.

So all in all, there seems to be no harm (hence Minor), but the output looks scary.