Problem
After import and placement of FBX meshes into a Scene in Godot Editor, a problem may be encountered when trying to save the project, either File » Save Scene or File » Save Scene As..., resulting in the following Alert message appearing;
Couldn't save scene. Likely dependencies (instances or inheritance) couldn't be satisfied.
Looking through the FileSystem panel, nothing seems out of the ordinary, meshes, materials, textures and other assets appear correctly (no special characters in files names etc.). Meshes can also be dropped into the Scene without issue (but may exhibit material appearance incongruities), scaled, manipulated or otherwise modified as objects. When selected however, the Inspector panel may display limited options, typically just position, scale and a few others, instead of the full set that includes Geometry, Skeleton and more.
Fix
To fix the problem, select individual meshes in the FileSystem, then in the Import panel ensure the Import As: property is set to Single Mesh. Click Reimport after making the change - meshes/object may need to be deleted and placed back in the scene.
This check/change needs to be performed on each imported FBX, or other model format (OBJ, glTF etc.), brought into Godot Editor.
Why does this happen
When Godot (v. 4.x series) imports FBX assets it defaults to setting Import As: in the Import panel to Scene, causing the incoming FBX be interpreted as Scene objects, an entity that ordinarily contains other objects and entities. When then attempting to save the project, Godot fails because its essentially attempting to save a Scene within a Scene - its trying to parse an invalid hierarchical, or improper dependency/inheritance structure - a scene within a scene recursion - resulting in failed saving and the Alert error.