### Godot version

4.01

### System information

Windows 10

### Issue description

It seems a tiles Custom Data is cleared/not set when "Local to Scene" is enabled for the TileMap in the Resource section. At least the custom data isn't set by the time of the _ready function in the script attached to the TileMap.

### Steps to reproduce

create TileMap and tileset with custom data and attached script. in _ready method attempt to read custom data from a used cell. 

In Attached project run it. It will print_debug if it found custom data or not. "Local to Scene" is enabled so it will not find the custom data.

### Minimal reproduction project

[TileMapCustomDataLocalBugReproduce.zip](https://github.com/godotengine/godot/files/11470771/TileMapCustomDataLocalBugReproduce.zip)

return tiles.has(p_atlas_coords);
}
Vector2i TileSetAtlasSource::get_tile_at_coords(Vector2i p_atlas_coords) const {
	if (!_coords_mapping_cache.has(p_atlas_coords)) {
		return INVALID_ATLAS_COORDS;
	}
	return _coords_mapping_cache[p_atlas_coords];
}
void TileSetAtlasSource::set_tile_animation_columns(const Vector2i p_atlas_coords, int p_frame_columns) {
	ERR_FAIL_COND_MSG(!tiles.has(p_atlas_coords), vformat("TileSetAtlasSource has no tile at %s.", Vector2i(p_atlas_coords)));
	ERR_FAIL_COND(p_frame_columns < 0);
	TileAlternativesData &tad = tiles[p_atlas_coords];
	bool room_for_tile = has_room_for_tile(p_atlas_coords, tad.size_in_atlas, p_frame_columns, tad.animation_separation, tad.animation_frames_durations.size(), p_atlas_coords);
	ERR_FAIL_COND_MSG(!room_for_tile, "Cannot set animation columns count, tiles are already present in the space the tile would cover.");
	_clear_coords_mapping_cache(p_atlas_coords);
	tiles[p_atlas_coords].animation_columns = p_frame_columns;
	_create_coords_mapping_cache(p_atlas_coords);
	_queue_update_padded_texture();
	emit_signal(SNAME("changed"));
}
int TileSetAtlasSource::get_tile_animation_columns(const Vector2i p_atlas_coords) const {