While noting I'm not an expert and the extension of stay stamps may well have variations per office, that extension of stay is significantly different to any stamp I've had over the years. There is usually several lines above but it could be the specific office. Also, unless L at the top of your pic might stand for LTR visa, the visa class is usually included in the extension stamp.
as I said, CM immigration requires a TM30 on file to do any transaction including visa extensions. You say you have been here 7 years and yet seemingly you've never heard of a TM30? Have you been living in a cave?
As for Bangkok check previous reports, they do sometimes require it
The unilateral demand you refer to is having a TM30 on file, a law that has existed since 1979. If you been here as long as you say, surely you would have had experience with it previously or at the very least read about it.
And as for "not required elsewhere," it has been in Chiang Mai for years - in fact, Ive just filed a 90 day report and it was the first thing they looked for, as with any transaction.
would depend on your visa/entry history. Presuming you don't have one before now, it won't be a problem crossing into Laos at the Chiang Khong/Huay Xai border and coming straight back. If you have a history of COVID extensions or volunteer visas, different considerations.
Jo is right but only the if you've already done one or two bounces (including flying out and then coming back - there's a limit of two per year at a land border), then you really should take a break before returning.
You will only need the TM30 for when you do your extension - CM Immigration insists on it. Legally, the accommodation provider is meant to file one within 24 hours of your arrival but not all Airbnbs do.