There seems to be an issue with Viewport node: if background is set to transparent, the glow is gone. Probably the best solution is to report the issue and wait for Godot devs to fix this one.
Other solutions:
set a background color/image for Inventory (this would ruin nice 3D world background)
avoid items with emission
use a texture from Player's camera to set a background for Inventory viewport (this way the background will not be animated)
use the same camera for 3D world and Inventory (this would cause a lot of issues with proper lighting and order of drawing)
Solution no. 3 (non-animated blurred background) seems promising. A shader was already proven to work fast enough for this purpose. Some notes:
since the shader works fast, maybe the background could be animated? That would require different camera management, to make sure that updated Player view texture doesn't include inventory view
the size of the blur has to be decided
no mipmaps are necessary for a blur shader, which makes it easier to manage the Player viewport texture
for some reason, the 3D quad mesh with a texture is much brighter than Player viewport texture, even though the shader has render mode unshaded etc. ; one of the workaround is to multiply the color by a low value (making the background darker, which actually works pretty well in this case)
There seems to be an issue with Viewport node: if background is set to transparent, the glow is gone. Probably the best solution is to report the issue and wait for Godot devs to fix this one.
Other solutions: