Latex paint is quite benign, and you can use darn near anything for a paint cup.
You're right not to paint out of the can. During the extended time you are painting with the can open, you have water and essential VOCs flashing out of the paint, altering its chemistry and thickening it.
Do not recycle any contaminated container... Food, oil, doesn't matter, wash it clean or don't recycle it. If you've been doing that all your life, time to stop. Recycling is an industrial process, where those clean materials are feedstocks into an industrial process which yields new, quality goods. The whole point is that this is much more efficient than starting with virgin petroleum, with all its geopolitical consequences. It defeats the purpose if process batches get contaminated. Of course they try to clean the material, but weird stuff can get by.
Latex paint can be cleaned up with soap and water, and it is not toxic to put down the drain in cleanup quantity -- do not dump paint down the drain. If I don't have potable water, I put the container and brushes in the trash/garbage/bin.
If you have a quantity of liquid paint to dispose of, the best way is to paint it on something you do not want, and throw it away (eventually). I have some old election signs with must be 30 coats of paint on em. Once when I did a cleanup blitz in the city, I painted over every illegal handbill within a block of my house. I didn't hate handbills, I just had a lot of paint to get rid of.