Interestingly, the issue is present in MySQL 5.7 and 8.0 as well, but only in those releases.

SET GLOBAL innodb_buffer_pool_filename='';

SHUTDOWN;

Leads to:

2023-01-24 15:30:26 0 [Note] InnoDB: FTS optimize thread exiting.

2023-01-24 15:30:26 0 [Note] InnoDB: Starting shutdown...

2023-01-24 15:30:26 0 [Note] InnoDB: Dumping buffer pool(s) to /test/MD090123-mariadb-11.0.1-linux-x86_64-opt/data

2023-01-24 15:30:26 0 [ERROR] InnoDB: Cannot delete '/test/MD090123-mariadb-11.0.1-linux-x86_64-opt/data': Is a directory

Bug confirmed present in:
MariaDB: 10.3.38 (dbg), 10.3.38 (opt), 10.4.28 (dbg), 10.4.28 (opt), 10.5.19 (dbg), 10.5.19 (opt), 10.6.12 (dbg), 10.6.12 (opt), 10.7.8 (dbg), 10.7.8 (opt), 10.8.7 (dbg), 10.8.7 (opt), 10.9.5 (dbg), 10.9.5 (opt), 10.10.3 (dbg), 10.10.3 (opt), 10.11.2 (opt), 10.11.2 (dbg), 11.0.1 (dbg), 11.0.1 (opt)
MySQL: 5.7.40 (dbg), 5.7.40 (opt), 8.0.31 (dbg), 8.0.31 (opt)

Bug (or feature/syntax) confirmed not present in:
MySQL: 5.5.62 (dbg), 5.5.62 (opt), 5.6.51 (dbg), 5.6.51 (opt)

Interface change: innodb_buffer_pool_filename is now a read-only variable