I created a second scene, which had a Node2D root. Its children were, in order, a TextureRect2D set to a noise texture (just to test this as I work), a SubViewport with with a MeshInstance3D torus and a Camera3D as children, and then finally a TextureRect2D with a ViewportTexture, set to that SubViewport. The camera was of course aligned to look straight down at the MeshInstance3D.
The viewport’s transparent_bg was toggled to on, and I can see the TextureRect2D right beneath it. Importing it as a scene tile worked fine, I can see the grassy green underneath the tile now.
It seems likely that I may have messed up my blending mode somewhere in the old one, which is fine; apparently I don’t really need to worry much about that.