It’s been a few years now, but when I was first looking I found my room by posting an ad on wg gesucht that I’m looking and shared the relevant info. My flatmate said she preferred to look that way, because it’s easier to find what she’s looking for and otherwise her mailbox gets flooded.

That said, with your budget also try immobilienscout24 and look for a whole apartment, the one I live in now is 700€/month and at the time of the paperwork my salary was twice that.

Last but not least - everyone wants to be in the ring. Try looking just outside of it, like Weissensee, Lichtenberg, Baumschulenweg, Schöneberg, depending on where your job is and what transit you need. It’s cheaper, there’s more availability, you don’t bump into tourist crowds when you carry your groceries home and you’re still pretty close to everything.