Solved! Go to Solution.
If you search for genre:"synth pop" you will get results (at least I do). No results for rock though, but I get a bunch of results for "soft rock", "hard rock", "pop/rock" and some other rock genres from this list. Not sure how up-to-date that list is though (it's actually the labels that provide this kind of metadata), I just tried some random genres. Note that you need to surround keywords that contain spaces with quotes, not the whole search query. Sorry if I confused you in my previous post.
I agree though that currently we don't have an easy way to browse genres and discover new music that way. Hope to get better at that!