I am currently on a visa exemption and have received a new passport (USA). It arrives with a letter to get your visa transferred at immigration. But since it is an exemption and not an actual visa, I'm okay right? I just depart the country as normal before it expires? (with the old passport in hand I assume, since that's what I entered with).
TLDR : Answer Summary
If you are in Thailand on a visa exemption and received a new passport, you can use both your old passport (which you entered with) and the new one to leave the country as your exemption is still valid. However, be aware that the rule regarding a maximum of two visa exempt entries by land border in a calendar year remains unchanged; having a new passport does not reset this limit.