What do I need for my first marriage visa extension in Thailand, and do I have to return to Phuket for it?

I see a northern border bounce in your near future.

No disrespect intended but if you weren't going to be able to stay IN that province until you got the year extension that was kind of a fail on your part to even start the process of the "marriage visa" 😕

I don't know any office that will issue the initial year extension on a Non-O visa based on marriage from another province so you're going to go back to Phuket to get that year extension. AND you should post on a Phuket group asking what documentation is required to get the year extension based on marriage to a thai

Now as far as your question, no one can tell, and you're going to have to go back to Phuket to talk to them about the process. I don't even think they'll let you apply for the year with a residence in Chiang Mai because you have to live/stay in the area where you're getting the extension.

Your other option would be to exit/re-enter the country (getting OFF this 90 day Non-O visa) and start all over again from a free stamp entry but this time apply at the Chiang Mai immigration office,

Why have you not filed a new address registration with the Chiang Mai Thai immigration office ?

Until you do, you are considered to be living in Phuket.

Where have you been filing the TM47, 90 day report ?

my 2 cents. You should visit Chiang Mai immigration and ask. It seems that it will be much more convenient to process visa and extension closer to where you live as it often involves more than one visit. Same for the bank.