How to check if my iPhone is network locked and request an official unlock?

This is a user to user forum, no one here can check if your phone is carrier locked.

How to unlock your iPhone for use with a different carrier -

How to unlock your iPhone for use with a different carrier - Apple Support

Carrier Lock:- Request your iPhone’s original Carrier to unlock your iPhone and if they agree and do it, then you may know the further process here --> How to unlock your iPhone for use with a different carrier ...

To be able to use any SIM across the globe you must have "No SIM Restriction" against Network Provider Lock. Please refer to the pic below.

Carrier Lock:- Request your iPhone’s original Carrier to unlock your iPhone and if they agree and do it, then you may know the further process here --> How to unlock your iPhone for use with a different carrier ...

Device Unlocking Policies | Verizon Privacy Policy

Unlock a Phone or Device - AT&T Device Unlock Portal

Unlocking your Sprint device - T-Mobile

FAQs about unlocking your Sprint device

Unlock Your Phone for Spectrum Mobile

If your phone in Settings > General > About says SIM Restrictions, your phone is carrier locked. The only entity who can remove the carrier lock is THE CARRIER. ONLY they can remove it. Apple can't remove a carrier lock. And if you are not a customer of the carrier, they are under no obligation to remove their lock. But if any money is still owed on the account, they may remove it for you if you agree to pay off any remaining dept.