Tiled not loading Tile Stamps from external tilesets #3808

Describe the bug In some cases Tiled does not not load Tile Stamps that use external tileset.

To Reproduce

1. Set the stamps folder.
2. Create stamps from external tileset, and they are working fine. Also, they are correctly saved in the selected folder.
3. Close Tiled and reopen the project.

Expected behavior Tile stamps should be loaded.

Specifications:

• OS: Ubuntu 20.04
• Tiled Version: 1.10.1 and 1.10.2

More notes

• If I open a new empty project, all stamps are loaded correctly. They will stay loaded if after that, in the same Tiled instance, I load the original project.
• Deleting .tiled-session and opening the project will load stamps correctly. This only works the first time when there's no session.
• I've tried using the session of the empty project that loads fine with my original project (with updated project filename and fileStates path to match), but it still does not work.

<details> <summary>Session of the empty project that loads stamps correctly</summary>

{
    "Map/SizeTest": {
        "height": 4300,
        "width": 2
    },
    "activeFile": "",
    "expandedProjectPaths": [
        "."
    ],
    "file.lastUsedOpenFilter": "All Files (*)",
    "fileStates": {
        "map/tilesets/tileset_outdoors.tsj": {
            "dynamicWrapping": false,
            "scaleInDock": 1
        }
    },
    "openFiles": [
    ],
    "project": "test.tiled-project",
    "recentFiles": [
    ]
}

</details>