Knapping, smithing, barrels, cooking, etc do not appear in JEI/EMI. Crafting methods from other mods (machine recipes, for example) still populate.

Looks like the isue is with EMI specifically, as running just JEI does not have this bug.

Do you run both EMI and JEI together, or just EMI for this bug to happen?
Because when I tried, with both EMI and EMI+JEI, I didn't get any of the recipe tabs.

emi doesn't have modded recipes compat by itself, jei is required for it, so yes you need to run both jei and emi for the jei compat to kick off.

I can recreate on my setup: being literally tfc + jei + emi

https://mclo.gs/F9gcIdM
vs the emi-less log
https://mclo.gs/yHvdK5X