I have Pehkui 2.2.1 with Forge 36.0.15 and when I launch the client it crashes to the Minecraft launcher halfway through the loading process with an exit code of 0.

I tried removing some other mods from the folder and I tried having only
Pehkui in the folder and the issue still occurs

And the launcher didn't give me an error log

Ok I updated to forge 36.1.32 and that fixed the crashing issue

I think your Forge version might be too old. Can you try again after updating Forge to 36.1.32 or newer?