Can I wear my Airborne and Air-Assault badges while in basic training?

It will likely just draw attention to yourself. Could be good or bad. Your Drill Sergeants, and the ones in your company will know you're prior service, even if you don't say anything. They have your records and they'll notice you aren't a dumb kid (like we all were). There was a dude in another platoon in my OSUT company who was prior service, same MOS, 11B the first time too. The Drills didn't mess with him more than anyone else, but they didn't show him any special treatment either. They didn't mess with him as much as the other trainees, but that is probably because he didn't make the same stupid mistakes.
I met a dude who was wearing his jump wings because he had been an ROTC cadet who left (or dropped out of for whatever reason) college and enlisted. I don't think it made much of a difference to anyone other than at the very beginning when it impressed the new trainees and probably got him a little crap from the drills demanding that he explain himself. So meaningless after like the second day.
The biggest risk of a problem I can imagine would be if you're not in your company area, without any of your drills around and another NCO or officer thinks you're faking it and you have to deal with the mess.

If you're trying to lay low and fly under the radar forget it... As a former MTI I can tell you your deportment will give you away anyway and yes, your DS will already have seen your records. Take the opportunity to share your experiences with the NPS recruits, it will be notices and appreciated by the DS.

I don't know you earned them and outside of the military they mean a lot but hey you are back in the military so that is where you wear in the military don't hide you past achievements be proud. If it were me I would wear them after all it is a fact ! Good luck to you soldier

Low profile to start with... The DI's will figure it out you been here before in no time

I would on graduation day!

I don't understand why they'd make you go back to boot if prior service. I could see wearing your bling once you're back active bit in boot? Probably not

Aren't you required to wear them if authorized?

Been there done that. Don’t. Drills usually expect that you’ll either be 1. Helpful to the class , 2. Absolute trash who will traffic in contraband and generally make their lives hard. Avoid making a spectacle of yourself, unless one of them finds out you have these awards and tells you to wear them (happened to me and one other guy)
Help the guy to your left and right, keep your head down nobody is too grown to clean and do push ups. Try to make the drills lives a little easier by helping privates avoid asking stupid questions and doing stupid things. Help with stuff like inventory. It’ll pay off at the end. Believe me.

Granted I'm older than Noah but when I went back into the Navy after a two year break we didn't go through full boot camp but shorter reindoctrination, there we were required to wear the posted uniform of the day, the wearing of warfare badges Submarine Dolpins in my case was required. Of course that was in 1983 so things might have changed.

Wear everything you are authorized to wear. You're not worried about a little smoke are you? You're going to get it anyway. Set the example and wade right in.