There isnt any way to add new apps directly to the tesla interface, no. Some people use the web browser / internet to do stuff, but thats not "add to tesla interface".
if your spotify icon disappeared from the bottom row of icons (in a model 3 or Y), you should be able to just open spotify again and have it show up there. If its gone as a source, you need to make sure you didnt disable it as a source.
