Mysql - when increase 'max_connections', what other paramters to adjust accordingly?
The main setting is innodb_buffer_pool_size.  It should be set to about 70% of available RAM if you have more than 4GB of RAM.
If you need more than the default 151 for max_connections it is worth looking into whether the client(s) are allowing too many connections.  It is better to reduce the load from that size.
A common problem is open_files_limit.  It comes from the OS's ulimit may be at a painfully low 1024.  That should be fixed in the OS.
There are no other &quot;likely&quot; settings to check on, especially with MySQL 8.0.
There are STATUS values that can help tuning busy systems.  See this for guidance in that help:  http://mysql.rjweb.org/doc.php/mysql_analysis#tuning