I'm running a modded server with some friends, and it seems when passing through the twilight forest portal, I'm unable to break blocks in the other dimension without relogging. I'm able to break in the overworld when returning. The same happens in reverse if I log in, in the forest and go back to the overworld.

Could be clarify on what you mean by "unable to break blocks"?
What do other people see when you're trying to break blocks?
How about block placement? How about interacting with blocks (in particular with buttons and pressure plates)? How about interacting with tile entities (in particular with chests and crafting tables)?
Does it only happen on the server and not in single player?
Is it only the TF portal and not the nether/end portals?
Please also attach your client log and the server log including the time at which you tried to break a block (preferably the entire thing).

All interaction with the world gives nothing back. I can try to open chests and tables, noithing. It's like I don't exist. I'll get back to you on the other prompts asap, I'm currently working on something.

Okay, right off the bat I can confirm it atleast does not happen when entering or leaving the nether, and not in single player, either. Sorry for spacing out the info like this. I'll send both the logs.
2020-03-27-3.log.gz
latest.log
I attached latest client and 2nd latest client.
latest.log
debug.log
And the latest server and debug.

Just had it happen in a singleplayer

Sorry for "Spam" I'm removing it from my server for now due to the issue among a couple graphical ones.

All interaction with the world gives nothing back.

Still not entirely sure what you're seeing. Is it like trying to break blocks in adventure mode? Like trying to break bedrock? Like the block's too far away (do you see the outline?)?
Do other people see you hitting the block? Can they see you move around normally otherwise?
If you log in while in the forest, then go to the overworld and from there go into the nether, can you break blocks?
If you log in while in the overworld with no forest portal nearby, then build a forest portal and immediately enter it without relogging, can you break blocks?

Is it reliable or does it only happen sometimes? (your singleplayer comment seems to imply the latter)

This may be a bit much to ask but I see no other way to get to the bottom of this: Could you try to remove third-party mods until you've found the minimal set of mods which still show this behaviour?