Should I apply for my COVID extension at Chiang Mai or Koh Samui?

For the visa question, you have to close the loop on the covid extensions at the same office, so when they stamp you and tell you to come back in 15 days (or however many Chiang Mai is) you need to do it at that immigration office. If you haven't had an issues with CM, I'd probably just try and do it here.

For the travel, probably going to have to take a bus to bkk and then a bus from bkk- surathani, then take the ferry over. There are some people in the Phuket Sandbox groups that take vans straight from Phuket to Chiang Mai, you might be able to grab one of those vans on the way back at a discounted rate.