What should I do about my visa and TM30 when I return to Thailand with a new passport?

An American expat on a NO Non-O Visa extension plans to travel to the U.S. to obtain a new passport. They seek advice on whether to indicate the new passport number on the TM30 form upon returning to Thailand, as the new number will not match their records. Comments suggest obtaining a reentry permit before leaving Thailand, carrying both old and new passports upon reentering, ensuring proper stamping at immigration, and visiting the local immigration office to transfer their visa extension to the new passport.