If you have access to some sort of basic Linux system (cloud server, local server whatever works for you) you can run a program on a timer such as isync.sourceforge.io (Debian package: isync) which reads email from one source and clones it to another. Be careful and run it in a security context that meets your needs (I use a local laptop w/encryption at home that runs headless 24/7, think raspberry Pi mode).

This includes IMAP (1) -> IMAP (2) as well as IMAP -> Local and so on; as with any app you’ll need to spend a bit learning how to build the optimum config file for your needs, but once you get it going it’s truly a “set and forget” little widget. Use an on-fail service like healthchecks.io in your wrapper script to get notified on error, then go about your life.