Technically the package responsible for connection protocols would be DBD::mysql, which hasn't had a release since 2019. But that module also lists MySQL 8.0 in the changes file, so it's at least known to work with the latest major release of mysql.

You might also consider relaxing the connection requirements on the server. I'm assuming they are forcing SSL by default? If you have a highly trusted network between your client and the server (such as 2 hosts with a shared vlan inside a firewalled data center) you could disable SSL for a small speed boost. Or, maybe it is some detail like requiring the latest TLS with the latest elliptic curve algorithm or something, and maybe you could relax that to more traditional algorithms.