When you export each section as a new scene, you’re saving it as it’s own individual object, no longer connected to the .blend file.
There is are two work arounds, both are a bit cumbersome
You can keep the .blend file saved in a scene, click the mesh node, copy the value, then paste the value onto the instantiated/local mesh node. This doesn’t update each file automatically, but it’s easy enough to keep everything stored locally and move things around as necessary.
Use the Linked library addon in Blender to be able to have a main blender file, but you’ll still need to save each individual object as a .blend and import it into Godot. The benefit of this is that you can edit the files rather quickly, without needing to manually open each file. It’s an Addon that needs to be enabled, then you need to go to file>Link>collections and add your objects from there. The only real benefit of this, again, is having one .blend file you focus on in blender.
I use a mix of both depending on what I’m doing but predominantly use method 2. This updates each object automatically in Godot
You can also write a tool script to automatically replace the mesh when it’s updated, I haven’t done this but it’s technically possible