Why does my rear cassette feel like it's jumping when I put pressure on small cog?
Those teeth are severely worn, just by visual inspection. Try a new cassette, chain rings, and chain. (Don't try changing just one.)

It could have been the grime that was holding the worn system together, and when you cleaned it all the play now shows up. In the future, if you replace your chain more often you can make the chain rings last longer.