What is your current immigration status other than TPS? If you are in F-1, go ahead and apply for a visa at the embassy. If they deny you visa, you can still use your tps ap to re-enter. Nowadays, official at TIA know what Ap looks like so it will be less hassle. Some ignorant will ask you, tapai ko gc khoi? Tapai ko visa khoi? Ask to see a supervisor in that case.
I recently travelled with tps ap, and it was a breeze. I was out of status for many years and currently was in removal proceedings before tps. After i got tps, i closed my case with the immigration court and traveled. US POE is super chill, wait in cbp room for 5-10 minutes and get your AP stamped. I wasn't asked where i went n how long. The only question i got asked was, did u see a judge?