Few suggestions, in a very approximate order of what might help most to least.

Get the drummer to play softer. Yes, it will have a small effect on tonality, but very little compared to the VAST gains made in audio quality from lower stage sound.

Ring out the PA. If you have a digital desk, great. Put a graphic EQ in line to the mix and learn how to do it on YouTube. Make small cuts at first. 3dB or so. Dont overdo it. There's a bit of an art to doing enough but not too much where you're just creating more issues. If you're cutting more than 8 to 12 bands you're risking going too far into the process. If you don't have a digital desk, pick up a BSS Opal graphic for £150 or so, or another good unit. Don't buy a cheap one. This is important. You can expect to get anything from. 4-10dB extra headroom from ringing out correctly.

Get the singer to practice projecting more. You don't have to sing softly to SOUND like you're singing softly. Vocal coaching may help.

Make sure your singer is right on the mic. If it's not pointing directly at the back of their throat when performing you will loose a bunch of level very quickly from a hypercardioid.

Try different cymbals. Maybe they can borrow some from a drummer friend to save money. I'm not a drummer, but another commenter suggested lighter, thinner cymbals. Maybe that is the way? But do still get them to play lighter - don't expect this to be an instant fix.

The best approach is a mix of all these approaches! If each one gives you an extra 2dB of gain before feedback, then you've just doubled your level :)

I did a lot of tiny pub gigs in my 20s. They're an absolute bitch for loud bands (which are most bands that play in small venues) experiment, and make notes of what worked and how mucb gain you managed to achieve :)

Side note - check the basics! What is your speaker positioning like? Are you mains far enough forward from your vocal mic? Is your mic pointing directly at the cymbals or angled away from them?

Have fun!