Please beware of overthinking and being overly critical about what you do for and with your son. Please beware of assuming too much that your own background makes you overcompensate, or that your husband's background means he's somehow "right" and you're "wrong" about what your son should and should not be doing.
Why spend time worrying that "I'm being too much of a mommy in certain things"? Why label it your own "baggage" if you simply like and enjoy helping him care for himself somewhat? That's not baggage and not babying -- unless you never teach him to do anything and won't let him try new things. You may cost yourself some precious and positive interactions with him if you stop helping him in the name of "he should be more competent at his age" based on something your husband believes.
Many seven-year-olds do dry themselves, and others don't, or do .some of the drying but stay damp enough that mom or dad helps out. That's not a lack of independence on his part or over-parenting on your part; it's a kid being seven and therefore not very interested in drying off and not very thorough.
Be careful that your husband doesn't push too hard, too fast for son to do too much on his own. A child this age is still close to little-kid age; expecting too much, too soon can make him insecure. Ask your son! "Hey, do you want to try that on your own this time?" He will feel like a big boy and has the option to say "Mom, can you help this time" if he needs to do so.
He should washing himself and brushing his teeth -- but you do need to ensure he does it, and check that he does it well. Don't hesitate to help him with flossing at least sometimes, which kids notoriously are bad at or just fudge and don't do. He should be washing himself, but again, dad should check in, "OK, time for underarms! Time for hair!" with good humor -- not necessarily doing it but cheerfully encouraging. (Again, if your son dislikes water on his face, he can't be left to wash hair all on his own, for instance.) He should be hanging his towels back up, or being sure he's not leaving wads of toothpaste in the sink. But he's not going to do it every single time; that's why you're there, just to remind him. It's not hovering; it's teaching.
Your son definitely should have specific and age-appropriate chores that help the household run: He can take out trash, pack his own bag for school, pack his lunch the night before (with your supervision; you don't want him to forget his homework or pack only gummies for lunch); put clothes in a hamper each day, pick up things, feed a pet, water plants (with some supervision so he doesn't over- or under-water; make it fun; get some of those devices that show when a plant is dry and needs watering so he knows when it's time). Create a chore chart so he remembers the chores and when to do them.
Praise him a lot, more than you think you need to -- your husband might feel that a lot of praise for "stuff he should just be doing anyway" is wrong, but young kids need the reinforcement of praise more than some adults realize. If your husband is the "I just did it because I had to and didn't expect praise" type -- you and he really need to talk about that and why praise motivates.
Never tell a child this age, "Clean up your room" or "clean up the living room when your play date's done." Those overwhelm even older kids because it's just too general -- where to start? Break things into specific tasks: Please put your books on the shelf and your toys in the box; I'll set the timer and check on you in 10 minutes. And so on. The results will be much better than huge, general statements like "Clean up your room."
And please stop second-guessing yourself so much. You're not preventing him from becoming a competent person by helping him learn self-care.