I bought the bundle last night. The issue with the Godot 4 exporter in Tiled is that the animated tiles are not in order in your atlas. The ones(alternates) that are lower on the atlas and have all the tiles in order from left to right will work. The upper left animated tiles where the first tile is separate from the rest of the animation strip will not work once exported to Godot because of the limitation in Godot's ability to only specify the first tile in the animation strip and the rest have to be in order without skipping tiles.
Its listed at very bottom of Tiled's Exporter help.
https://doc.mapeditor.org/en/latest/manual/export-tscn/
I will probably just redo that PNG so that i can use all of them. If you could keep them in order for your future work, it would make them compatible.