Issue :
It is impossible to play the mod in 1.20.1 with forge because it is only available with neoforge, WHICH DOES NOT EXIST, Neoforge only starts at 1.20.2.
The game does not load with mod version "1.20.1 neoforge" and forge loader, and it doesn't load either with neoforge because neoforge is 1.20.2.

Solution :
Make a forge version of the mod for 1.20.1 instead of neoforge.

PS: How the hell did you guys manage to make a version of the mod on a loader that doesn't even exist ???

Neoforge is available for 1.20.1 it just seems they've delisted it from the public download page, though it is still available via their maven. It seems the Neoforge team don't recommend using it for 1.20.1. But that does not matter as Forge and Neoforge mods are compatible with eachother's loader on 1.20.1

If you want to use Forge/can't find the Neoforge version you can use the 1.20.1 builds with Forge (I believe the builds are listed as compatible with both on Curseforge and Modrinth), it works fine.

I tried meddling more with my install, now it does load indeed, but not when I also have Anvil Fix (from Up) loaded, which works fine when Aether isn't loaded. So this looks more like a comptibility issue between Aether and Anvil Fix.
Edit : it seems to work with fabric version of Up's Anvil Fix (from bsasealteam6) ported to forge with Sinytra Connector.

Should I open a new issue for compatibily ?
Sorry for the bother.