On a hobby project recently I've only written backend integration tests. I found these to be extremely useful though since they touch directly or indirectly to all the critical parts of the software, so if something's broken it will eventually be caught there. Also since it's relatively high level there's also rarely a need to change them whenever I change something to the backend. All in all it's definitely a time saver, both in terms of catching bugs and maintaining the tests.

I think there's still a value in detailed unit tests but mostly for library code, when you want to test each function properly with various inputs.