Alright, so I tried removing just Carry On, then added Carry On back and removed Valkyrien Skies and other mods related to it, and then I removed both Carry On and all Valkyrien Skies mods (log: https://mclo.gs/bqRBmKP) and still got the same issue with Unknown serializer codes 109, 111, etc. in all instances.
There seems to be some remnant files of Valkyrien Skies in other folders that I didn't remove but, I really feel like the issue is just with Cobblemon. I was willing to get rid of those mods if Cobblemon worked with them but it didn't. I specifically had a version of the server without Cobblemon at first but then added it in and that's when I started getting that error, and when I would remove it from the modpack, everything worked perfectly again.
This is really strange honestly. I had my friend try joining the server with the modpack with Cobblemon in it. His computer runs on Windows 10. He was able to join without disconnecting, and everything seems to be fine, he's able to play (log: https://mclo.gs/RkLxaOT). So, it must be something between Cobblemon and Windows 11 not allowing it to run correctly??? At least some of the blame is seemingly on Windows 11. I have no idea of what to do now to fix this issue for myself though, other than I'll try to do a Windows Update to see if that fixes anything for me. This is so weird, but you testing it with your friends that run it on different OS was an interesting step in the right direction.
Anyone please let me know of any other potential solutions. I really want to play on this modpack with Cobblemon, since my friend is able to play with no issues and now it's just me on Windows 11 that isn't allowing it to work.