When using a resource pack, at least in the Fabric version, which changes mob models, as far as I can tell the healthbar tries to show the vanilla model with the modded texture or something, causing all sorts of visual issues from massively stretched flat planes of texture, to jumbled limbs and half-missing textures. I am, unfortunately, using Optifine and Optifabric, since a lot of the resource pack features don't work without it and have no alternatives.

If this isn't fixable on this mod's end, could there at least be an option to turn off the 3d mob portrait?

You can turn off the entity model using hud.showEntity: false

This might be fixable on the mod's side. Could you upload a version of the resource pack here?

Assuming this worked as I haven't heard back.