Your US Embassy will provide a letter to the RTP Immigration to transfer your Visa Stamps.
Take this letter, your old passport and new passport to IO and they will transfer the "Visa stamps" for you, for whatever fee is charged.
But as Sebastian has said bring all your documents with you, have them photocopied, sign each copy with blue ink pen. (Even take a copy of your new passport application, you won't need it but you could be asked for it including the receipt, maybe even the envelope it came in...) The IO's basically can ask you for anything!
As Stuart has said nothing should prevent you doing this....but it's always wise to check with your IO because rules can be interpreted differently from office and by officer.
Have you checked the websites of each major Thai bank? That way you should find the most up to date information for your enquiry? You should find most websites available in English.
Scott Williams You need to act without delay if you don't want to be pinged for overstay.
As stated report Passport Lost / Stolen to RTP.
Take this Police document to the UK Embassy and request an ETD.
This will permit you to travel back to the UK unhindered.
You are gonna have to get your skates on with booking a flight back to "blighty" before the end of 5th January 2023.
You can possibly start the online process of getting a replacement PP, once you have your RTP report to scan and send your new PP to an address in the UK to be picked up later.
Then once you have your new UK passport you can return to Thailand and start your "Visa" process all over again.