Would it be possible for Palmyra to survive as an autonomous territory within the Roman Empire sharing authority and power with the Emperor while maintaining the territorial gains it made during the crisis?
Aurelian seems to have never accepted the situation, and safe a real submission of Palmyre which would IMO likely take the form of giving up at least Egypt. When Aurelian would have dealt with usurpers in Gaul, the next target would always be a Palmyre with any pretense of imperial autonomy. At this point of the crisis, it would have been hard to have both a strong Palmyrenian polity in the east and a strong enough Roman Empire.
A relatively weak enough Roman Empire eventually means Zenobia could pull a Septimus Severus, so the window of opportunity is kind of reduced.
I think you might need two different pods : one where Odaenathus is spared assassination and continues his policy of cooperation with Rome while having a distinct and legal power over Oriens. The second, with a slightly worse IIIrd century, where emperors have more trouble to manage the return to order in Romania and rely more on deputies (like Odaenathus, or Carus/Numerian) which would create a systematisation of "duchies" or "vice-imperium" so to speak, possibly fueled with Barbarians being more able to settle Romania in the same period and creating entities not as foedi but as "duchies" they could dominate the hierarchy (as Franks did in WRE in the IVth)
Then Palmyre would survive as with her king as permanent "Dux Oriens" of a half-federal Roman Empire. Sort of a tetrarchy on steroids born out of necessities and realpolitk.
That's a long shot, but not implausible IMO. Just don't expect it to be stable. Either the emperor got the best out of it and only some periphery areas remains, either one duke gets better of it and become emperor, either it all comes down like a house of cards (with in the best of case, the emperor as a regional power technically overlording what remains from afar and more often than not replaced).