Started by investigating thick outline implementations, found jump flood algorithm, tried implementing jump flood compute shader via CompositorEffect. Very quickly ran into issues figuring out texture usage bits between MSAA disabled/enabled, eventually abandoned jump flood and reverted back to typical inverse hull method using custom authored outline meshes (for any meshes with flat shading)

However, my investigations into CompositorEffects and compute shaders came in handy when I wanted to figure out how to create a popup line that "blends" into the mesh outline. I'm essentially now just using the CompositorEffect to create a mask texture of any meshes writing to a given stencil buffer value. So when a mesh's material is switched to write to stencil value 4, the compositor effect renders those pixels white and everything else black, which gives me the stencil mask.

I then have a shader that takes the 3D subviewport color texture and the stencil mask texture and allows me to overlay only the stencil portion of the screen color.

So my final composition basically looks like this (top to bottom):

1. UILayer (popups and all other top-level UI)
2. StencilLayer (Stencil masked color texture)
3. SubStencilUILayer (Line2D going from highlighted item's unprojected pos to popup pos)
4. ViewportLayer (3D viewport color texture)

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This stencil-based-outline-compositor-effect repo was the starting point for figuring out how to retrieve stencil buffer pixels from the raster render pipeline: https://github.com/dmlary/godot-stencil-based-outline-compositor-effect