Is it possible to leave active duty Navy as enlisted and commission into the reserves of the Air Force?

You'd have to break Service and be accepted to an officer producing program: OTS, Academy, ROTC, direct commission (usually Chaplains and Medical specialists). Have you reached out to an Air Force recruiter / ANG Recruiter?

There is not a way to transfer between service branches like you describe. It's usually something narrow like pilots. USCG had a poaching program to grab Army Warrant rotary wing pilots and direct commission them.

https://www.airforce.com/how-to-join/process/officer

Look carefully at age requirements and age waivers for AD service.

It certainly is possible, just remember the needs of the service and if your flexible you should be able to commission. A few possible hurdles to overcome; a bachelors degree can open doors however these days specialty degrees are very desirable, age waiver for years in service, making yourself competitive so do your homework on AF AFSCs, and have references lined up when you're close to separating from USN.

Enjoy your next 4-years, they will fly by as you begin outlining your future. I wish you all the best!

This is done all the time by Mustangs such as myself. Had time left and was accepted into a commissioning program. Perhaps a couple more hoops going to a different service. Just make sure you're dealing with a real accessions officer for the program you're looking at. They deal with whatever releases and other paperwork needed all the time as well. It is typically outside the knowledge and authority of general recruiters. One thing to make sure of is, when you shift over, make sure they get your TIS/PEBD correctly calculated and carried over. It that is botched, it'll take a Board of Correction to fix.