Yes—an XMP sidecar can, in principle, be shared by multiple files that have the same basename but different extensions, because the XMP sidecar itself does not contain a built-in reference to one specific original file.

What likely caused confusion is tool behavior, not an XMP limitation. ExifTool does not normally overwrite an existing sidecar when writing metadata. It reports whether it created a new file or updated an existing one, and when updating, it adds or changes tags as needed while leaving unrelated existing tags alone. If you try to create a sidecar from scratch with a filename that already exists, ExifTool will usually report an error rather than silently replace it.

So for a Live Photo pair like IMG_1000.JPG and IMG_1000.MOV, a single IMG_1000.XMP is possible. Whether that works well in practice depends on whether your software expects one sidecar per asset or can interpret shared metadata consistently.