An API error is later than a loader error
Start by naming the layer that already works. If Minecraft reaches the main menu, the Verity entry appears in the mod list, the world opens, and the box or entity appears, the base installation has passed several checks. If a prompt then produces an API connection failed line, the immediate problem is probably not Forge, the Verity JE jar, or the world save. It is the provider path used after the character tries to answer.
If the game crashes before those steps, use the Java version route instead. The current checked Java file is verity-5.7.3.jar for Minecraft 1.20.1 Forge. The project page still lists the 1.21.1 NeoForge branch but warns that it is deprecated and has many bugs. Do not combine a 1.20.1 Forge file with a 1.21.1 NeoForge profile and then diagnose the result as an API problem.