I'm interested in tournaments where you can participate even without a new deposit. For example, you play with your remaining balance, but still get into the tournament. I often see that you have to make a deposit to participate, and this is a bit annoying. Are there sites without such a restriction?

Yes, PinUp casino holds tournaments where participation is possible simply for playing a certain slot, without a deposit on that day. It is enough to have a balance - you play and participate. This is especially often done with new slots or as part of seasonal events. The prizes are real, sometimes even without wagering. I participated in one without a deposit and took 5th place - I received free spins and some cash.