As for the certificate of residence: It is supposed to be free of charge. BUT if you really want it for free, they say it is going to take a few weeks. If you pay 500THB, you can come in and collect it the next day. Welcome to Thailand.
Chiang Mai is a yes for the annoying āunder considerationā, unfortunately. Usual documents (passport copies, image, TM30 and forms they give you). No embassy letter. At least it was like that.
Typically all you have to bring next to your passport (+ copies of its relevant pages) and a picture is a current TM.30 (proof your current address being reported). The actual forms required vary by immigration office - but will be handed to you there. Some IO additionally ask for a letter of your embassy or an email of that embassy stating that they are not issuing such letters. For exact current requirements in Phuket - maybe someone else here knows more details.
Usually you would need to leave immediately or you could apply for a 7-day grace period @ 1,900 baht. Currently though, there is COVID 60-day extensions, which can be applied for at the same time of terminating the NON-B. Should give you 60 days for getting everything required for a new NON-B. So current situation should actually work in your favor.
Most immigration offices do NOT require separate 90 day reports while on 60-day COVID extensions. Does not make sense anyway, since it is in the very nature of 60-day extensions, that you report and proof your current address every 60 days. Other immigration offices however seem to do require separate 90-day reports even on (in between) short term 60-day extensions (lastly heard so from people on Phangan / Koh Tao). The usual inconsistent mess. So it will depend on where you do your next COVID extension. You may or may not be fined 2,000 baht.
If you cancel your job / your job is terminated, and the job was the only basis for your permission to be in Thailand, then normally you would have to leave Thailand right away - on the day your job is terminated.
There is no changing to tourist visa inside of the country. In normal times, you could apply for an additional 7-day grace period @ 1,900 baht.
In current covid times, you can apply for a 60-day covid extension of stay right after your current / work related one is cancelled. So right now you could achieve staying longer even after stopping your job.