Can't connect to MySQL server -- server out of memory

I regularly need to copy "big" tables from a MySQL 5.7 server (Windows) to a MariaDB 10.6.10 server (Linux). I am trying to implement this using CONNECT tables defined on the MariaDB server reaching out via CONNECT tables to the MySQL server, doing a simple insert into linux_table select * from mysql_table_connect, where mysql_table_connect uses the CONNECT engine to access the table on the MySQL server.
This generally works fine for tables up to several millions of rows, but it fails consistently for tables containing more than 14 or so millions of rows.
First, I get a message Lost connection to MySQL server during query. On trying to establish a new connection to the Linux server, I then get Can't connect to MySQL server on '...', where ... is the name of the Linux server.
My monitoring system tells me at about the same time that the Linux server is running out of memory.