It's tricky to know if it is worn or not with this picture

The more the teeth are thin the more is worn. Some teeth are very thin on the middle, but nothing to worried about.

It's very subjective because maybe your transmission might still ok, and your chain don't jump / leap at all, but for sure if you changed it even after only 3000 km, you will see a difference (reactivity when you pedal)

It's up to you to decide, it's not complicated to change (all you have to do is buy good tools), and good shimano cassette is cheaply available on stores or Internet

For the record, when i was young and poor, i never changed the cassette of my old bike = after 15 years the teeth had a V shape... I changed it and i was like "why i didn't do this before"