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

Personally, I would rather fly under the radar and not draw attention to myself. That's me personally. You earned them so if you choose to wear them, nothing wrong with that. As has been said in other comments, just be ready for added responsibility or possible harsher treatment, for various possible reasons. When I was in Basic/AIT at Knox in the 80s, there was an old vet that came back in and he got nothing but respect from Drill Sgts. and the rest of us. He had a chest full of ribbons and was Ranger, Special Forces etc.

Wear them, you earned them.

Update* I just got back from BCT and I wasn't allowed to we wear rank not any badges and combat patch because I was an E-4. There was an E-6 also there in BCT and he was allowed to wear all his badges. The drills found out I was prior service the first week I was there hahahaha. The way they found out is because one of them asked me for my name... instead of me saying "Trainee and my last name" I said Specialist and my last name.

They're already going to know. They're going to ask if anyone is prior service and single you out at first. Fuck it, show these recruits what basic is and what you CAN do. Basic is easy already

I agree with the Lt. Col
I wouldn’t.

Couple of questions. One, what is the Uniform of the Day in Basic? Will you be allowed to wear your SPC stripes (You may then outrank the Assist. D.I.). Do you have to maintain Qualifications for Airborne, and Air Assault. And what does the command recommend. I know, that even though I went into Boot Camp as an E-3, I wasn't allowed to wear the stripes until AFTER Graduation (This was 40+ years ago though...)

Wear them proudly, you earned them!

When I went to USAFR after 13 years from active duty separation, I had a new AFSC and went to tech school. I was the only one in the class with a National Defense ribbon. That was nothing. We sent a MSgt with the new AFSC and he had a Purple Heart. He was wounded at the Battle of the Bulge. This was 1984.

I believe if you earned them, wear them, but don't be surprised if you are informed that you may have to wait until you get to a later point in training before you can wear them...

Wear your badges! I was in a similar situation, but with a difference. When I came back in after a break in service, I was, like you, an E-4 (lost a stripe when I re-enlisted). I was made "platoon guide" and wore an armband with SGT (E-5) on it. But because my platoon weren't sure whether to call me sergeant or specialist, I stopped wearing my specialist insignia until we graduated.
In your case, there would be no confusion, so I say again - wear your badges! You earned them!