Ours moved home right after college - he started a job with a good company but his ultimate work location was "iffy" in the beginning while he was training. So he lived here for 8 months until he got settled and then found a room in a friend's apartment. That was 3.5 years ago. In June, there was a bit of a crisis in his new apartment so he moved home temporarily, anticipating getting a place with his girlfriend. Stuff happened, they broke up, and so he's actively working to find a place on his own without her in the picture.
The first time was a little dicey - he had the "I'm an adult" attitude with the attendant "I can do what I want" mantra. We did charge him rent and he was fine with it, and we also had to learn to let go of things like expecting him to be home for dinner or whatever. He'd been on his own for 4 years at college with no curfew, so we learned to not be parents in that regard. We didn't plan on him for dinner - he could fix himself something when he arrived, or he could go out. If we had leftovers, he was welcome to them. He'd been doing his own laundry for years (since he was 15) so that was simple to continue. If he left stuff in the washer or dryer and we needed to use them, his stuff got dumped in a laundry basket and he could deal with it on his own terms. We stayed out of his room but closed the door if it was messy.
The second time he came home, it was totally different - he'd been on his own for a long time and he was grateful that we helped him in an emergency. We supported him emotionally through the breakup, but he also was an enormous help to us when my husband developed a rare medical condition that landed him in ICU and so forth. He doesn't pay rent this time, but he has taken on certain bills (substantial ones) so it works out. We allowed him to put a lock on his door so it's more like his own apartment. The restriction is that he cannot lock it during the night - if there were ever a fire or a household emergency and we couldn't get in there...
I would say your son should pay rent, at least on his room if not counting the common areas. Give up on telling him he has to keep it clean - just shut the door and do not go in there. Anything he did for himself at college, he does for himself at your house: housekeeping, laundry, meals. I don't think you can micromanage his "eating habits" whatever that means, but you don't need to buy junk food for him if he only wants frozen pizza and mac/cheese. He can buy those things himself. When he runs out of money, that's on him.
I'm not sure how you plan to police/supervise 4 hours a week in chores. If he doesn't do it, then what? You nag him like he's 8 years old? That just makes everyone miserable. I think it's better to give him certain ones regardless of how long they take - dishes in dishwasher, trash on trash days, whatever your needs are. "Clothes out of dryer is fine" but if he doesn't, you're stuck with no dryer! So just dump things on his floor or put them in a heap in a laundry basket (if he has his own bathroom, put the basket in his shower!).
Our son has a TV in his room (he bought it) and he pays for the cable now plus the WiFi (which we get to use elsewhere in the house). If he doesn't pay it, he loses it too, not just us. So there's never a problem. He does all our technical stuff with computers - a huge help. He does yard work and home repairs, and he pays for trash pick-up/recycling.
Food - I shop and he's responsible for putting stuff on the grocery list when we're low - especially fruit and yogurt, which he inhales. If he wants weird stuff, he buys it himself - but he also usually texts me and says he's going to the store so do I need anything too. He eats out a lot or they bring in sandwiches to his work, so he doesn't eat a lot.
We let him half his girlfriend overnight - we weren't going to police his sex life since he'd been on his own for 4 years. We happily showed her where the clean towels are. I did tell him I expected to be told when she was coming over and I wasn't cleaning the house on her behalf! We absolutely don't ask him when he's coming home although if I'm cooking something special I tell him it's on hand and he can have some - as a result, he usually reciprocates and tells me what he's doing.
I think, if your kid has improved in the maturity department, you can celebrate that. I don't think you can really tell an adult child to have a savings goal, and I think you have to watch the advice-giving! You have to try not to mother him all the time - and that means not making his dinner or cleaning his dishes or whatever. He's an adult - treat him that way. You want a shift in his attitudes, but you need to make one in your role as well. But he's a tenant, so he has obligations. Make up an agreement if you want, but make it based on money as well as the common areas (he can't leave his stuff everywhere). Figure out what you're going to do if he doesn't get paid - as a landlord would do.