Replace Lightning Fabric by elementary setup

**Is your feature request related to a problem? Please describe.**
We've had many problems with Lightning Fabric doing thing behind the scenes. Right now, we only use it to spawn processes for the different ranks. This does not justify all its hidden complexity.

**Describe the solution you'd like**
Replace all Lightning Fabric dependencies by `torch.distributed` and `torch.multiprocessing` basics.

This could be done by asking Claude Code to do it.