I have a speculation, that using the latest version of MultiConnect makes this mod a big issue.

When used alongside each other, some sort of error occurs when you manually leave a server with the disconnect button, and AutoReconnect will try to put you back into the server, as if you were kicked out.
If you click back to the server list with the button within the time limit of being reconnected, your account will connect to the server, but the client will remain in the server list, and the account will stay connected until you close Minecraft entirely.

Now, here's the fun part. If you instead join another server, your account will technically be in both servers. You can move around on the one you just joined, and there will be several glitches, including the skybox alternating between the ones on the two servers.
I have not tried it with three servers, and I don't want to. My computer doesn't like me doing it in the first place.

Point is, you have to fix it. MultiConnect is the only mod that seems to be doing it, but I have some other mods enabled too, which could be contributing to it. I will come back after I've done some testing.

Update: After trying launching with only MultiConnect, Fabric API, and AutoReconnect, it seems to be another mod causing it. alongside AutoReconnect.