Ahh, okay I believe this might be an issue I've already run into to some degree: https://itch.io/t/1290294/quads-not-working-with-urp-in-ui
It seems that Unity 2021 has some issues with rendering multiple materials on the same gameObject... it's been a few months into 2021 now, so I should probably try contacting someone at Unity about this. For now, all I can really recommend is sticking to Unity's LTS releases (2018.4, 2019.4) if that's a possibility. Other developer friends have told me that 2021 has a ton of odd things going on currently.
Is this happening with just URP/HDRP, or is this with the standard 3D system? This will help me file the report to Unity.
Edit: Checked with other asset devs too, and it appears that Unity 2021 is a "tech release stream" so it's still in beta and a lot of stuff doesn't work. If possible, try one of the LTS releases!