Tiled ships with a plugin that enables direct editing of Stardew Valley maps (and any other maps using the tBIN format). This plugin needs to be enabled in Edit > Preferences > Plugins. It is not enabled by default because it won’t store everything (most notably it doesn’t support object layers in general, nor external tilesets), so you need to know what you are doing.
The tBIN format supports setting custom properties on the tiles of a tile layer. Since Tiled does not support this directly, “TileData” objects are created that match the location of the tile, on which such properties are then stored.