Right clicking doesn't select any items and shift right clicking makes the gaining xp noise but nothing else happens. I've tried with ingots, coal/charcoal, wood, and diamonds.

Can confirm. Could this be because the tomb of alkehestry is disabled there is nothing to burn?

that actually is likely as it works off of alkahestry recipes which likely don't load. I have changed this over to a list of items to experience in config. it's done in dev and should be releasing that soon

this is now fixed in the latest release on curseforge