If you can provide a certificate of residency (done for 300 Thb at the immigration), you can go to ANY BRANCH of ANY BANK with your passport and open an account and get an ATM card on site in 30 minutes, no headaches , no particular insurance to buy.
It doesn't change anything to all I said as technically, an extension of stay IS a new visa (new stamp, new number, new date of start, new 12 month validity, new expiry date, all that exclusively attached/limited to the passport it was applied for and until that passport expires if meant to happen before the visa does).
A CURRENT visa can always be transferred to a renewed passport.
BUT, a NEW visa can never be transferred to a RENEWED passport. This NEW visa will always be attached and limited to the passport it's been done on/for, until the last day of the current passport validity MAXIMUM..
But, to enhance the presentation and clear your conscious at the same time , just buy yourself a nice suitable passport cover. (you can easily find that online, Lazada or what). It's a perfectly sized and ready to use (decorated or not) cover, you put your passport in just like a dress.
It will dress your passport and also protect it from any additional damages.
The correct way to handle this (and everything else happening to you in a foreign country, for that matter) is to adopt the proper way to think about it FIRST.
And to do so, you absolutely need to delete that formulation "in the States (or else ), we bla, bla bla ... " from both your HEAD and your VOCABULARY, or life will undeniably be much much harder as an expat anywhere you CHOSE to settle.
New Place = New Rules = New Laws = New Customs = New YOU.
I figure it says that cause as the visa IS already multi entry, you're exempt from purchasing an additional multi entry permit.
Anyway, you have ABSOLUTELY no worries to hold concerning this matter as TWO of the "privileges" this visa is promoted on are CLEARLY the fact that THE 90 DAY REPORT IS EXTENDED TO 1 YEAR and THAT THE VISA IS MULTI ENTRY.