Linux

Don't know of a solution that does this, but you could solve it with a two-step process. First, rsync the files to the server as-is, then use a background job on the server that converts lossless to lossy every hour or so.

Storage is really cheap these days though, why compress lossy in the first place?

Why use git exactly? You're never changing the content of the files themselves (excluding the effect of lossy compression) so you also don't need to track those changes, right?
This seems more like a job for rsync.

Aside from that, I don't know more for how to achieve the full setup you're trying to create, sorry

I want to convert all lossless files to lossy, preferably before uploading them

so it's not exactly a mirror, right?

here's an idea:

• A - the source containing lossless files
• B - the local storage of lossy files
• C - a remote mirror of B

With that, you can do:

• A -> B: a systemd service that makes this conversion.
• B -> C: git or syncthing to mirror and/or version control.

This uses more storage than you probably intended to (lossy files are also stored locally), but it's a mirror.

Make a script. I'd use xonsh or python with sh.py.

• create a dict for remote to local filename map
• walk your local collection
  • for each file, determine what the correct remote name (including a valid extension) would be, and add the pair to the dict, with remote filenames as keys, local filenames as values
• make a set like local_munged_names from that dict's keys
• walk your remote tree, and store the filenames in a set like remote_names
• names_to_upload = local_munged_names - remote_names
• for each name in names to upload, look up the local filename from the remote to local filename map. Then, encode it if it needs encoding, and upload.