Is my iPhone carrier unlocked

I have been with AT&T for 11 years (and 6 iPhones through AT&T, most recent iPhone XS was through Apple though) and they do not automatically unlock a device just because you’ve paid it off. You must use their web form to request an unlock - https://www.att.com/deviceunlock/#/

Once you get an email that it’s done (or check again later online - it usually is less than a single business day), you would restore it as a new device in iTunes. At the end of the restore you will see a message in iTunes confirming that the device was unlocked. If you don’t see the confirmation message in iTunes, it’s not unlocked.

You cannot restore from a backup first to process an unlock. You must restore it as new, which erases it but processes the unlock. After that, you can erase all content and settings and go through setup again, restoring from your iCloud backup.

The message in iTunes is something like “congratulations: your iPhone is unlocked”.

If you have AT&T cellular service, your iPhone automatically becomes unlocked when your service contract expires and you have no outstanding payments due. In other words, at the termination of the contract, you're automatically placed on a "month-to-month" service "plan" and your phone is unlocked. You can test this by switching out your AT&T SIM card with that from another carrier. Note that your AT&T phone works with GSM and, in theory, should work with any other carrier that also uses GSM. Service providers, that rely on CDMA, will not work with this phone.

On the other hand, if you still have an active contract you will need to contact AT&T to request an unlock.

FWIW, my iPhone is currently on that "month-to-month" plan and I have verified with AT&T that it is unlocked. There wasn't anything I had to do to make this happen. On my phone there is nothing showing as "Carrier Settings," only "Carrier Services."

Use the Contact Support link at the top of this page and ask Apple to check the lock status. If you restored the phone as new and did not get that message your phone is not unlocked.

FWIW. I will be traveling to Japan this fall and have tested this with a Japanese cellular SIM card. I have an iPhone SE and it worked. I then replaced it with my AT&T SIM and got my AT&T service back ... so it worked in my case.

Not disagreeing with you, but it worked in my case. The only difference is I purchase my first iPhone (iPhone 4) directly from AT&T on a two-year contract. I don't use their AT&T Next plan. Since then, I purchased newer models from the Apple online store and Apple took care of re-upping my AT&T contract. This was the first time, in all those years, that I needed to use a different carrier's SIM for extended travel with my current iPhone SE. Since my last two-year contract expired over a year ago, I was automatically switched to a "month-to-month" plan by AT&T. When I contacted them, they are the ones that told me my phone was "automatically" unlocked at the end of the contract ... and my "switching SIM" test worked. So, maybe, I'm the exception and not the rule? I have to agree with the OP that AT&T does not make it very clear, and, of course, would prefer that you use one of their "travel" plans instead.

Only the carrier that locks the iPhone can officially unlock.

Start here: https://www.att.com/deviceunlock/#/

As far as I know, AT&T has never magically unlocked iPhones when the contractual obligation was complete.

I have 5 phones on my account. 2 of which are fully paid off, all purchased through AT&T Next.

I'll have to check the status of the 2 that are paid off, but the last time I rolled over phones that were paid off, I had to manually request unlocks from AT&T.

If you don’t have an alternate carrier’s SIM, then the second instructions are right. As I mentioned, you first have to erase it (restore as a new device in iTunes). Then restore a second time using your iCloud or iTunes backup.

You do have to restore it as a NEW iPhone, not from your backup.

AT&T's traveler plans are pretty good, and least for short trips. You keep your number, and you keep your plan for $10 a day for any day you use cellular voice or cellular data. You don't pay for Wi-Fi data or voice over Wi-Fi. I used to carry a separate phone with a local SIM, but the new plans are so reasonable I don't bother.