Please stop taking his behaviour so personally. He is the same with everyone, after all. You have been really nice to him, but as you say, he's thrown it back in your face. So it is time for a change.
Actions speak louder than words. I find them easier than words, too! So, with the washing (assuming this was bil not DH?) I would've felt angry and humiliated, like I think you did, but I would've moved the bag from the kitchen back to his room. Actually, it's time to start refusing to do it, like you and your DH have agreed. Mention that in the talk you're having, so then if he brings you washing, you can just put it back in his room. No need for uncomfortable conversations, then.
To make this talk you're going to have easier (and I do think your DH is passing the buck getting you to say it), write down the expectations and check with DH that he agrees. Then the talk just needs to be: DH and I have talked and this is what we expect of you if you want to keep living here. One sentence, very clear.
But you have to be strong. Don't think, "well, I don't really mind, I've done it before." This is your new start for 2021 and it'll be a great year for your dignity and self-respect.
I think you'd feel happier if you stop picking up dirty socks from the floor, too. Anything that feels demeaning - stop doing it. If your DC do it, go get them, take them to that room and ask them to put them in the bin. (With small DC, if you think they won't, it helps to say, "and then we'll (go to the playground/watch your favourite programme/insert thing they like doing here.)") With DH, either leave the socks there, or move them to somewhere more convenient for you - a box on his side of the need, maybe. Only wash things which are put in the correct place.
The great thing about all this is that nothing needs to be said. Occasional reminders, maybe, no more than that. You decide what level of respect you deserve and you stick to it.