Then it almost certainly has a freewheel (not a cassette). At the bike co-op, we end up with lots of stiffly turning 30 year old freewheels. The grease dries out and turns to paste. However, this usually happens to components that haven't been ridden in years. They can be freed up by dribbling in some oil.
You could try oiling your freewheel (without even taking anything apart): Lay your bike down on its left side (so the gears are up). Dribble some oil onto the "side" of the freewheel just within the smallest cog (gear). One part of the freewheel turns with the gears, and another turns with the entire wheel. You want to apply oil at the tiny gap between those parts. For the oil, you can probably use chain lube (unless you use a wax type lube).
Because your problem developed on an actively ridden bike, I'm suspecting a different type of failure. Perhaps, as Eden wrote, the pawls are breaking. Maybe some sand got in there. Possibly the bearings have failed.




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