The 60 day SETV is really of no use to anyone from the 93 countries that can now get 60 day exempt stamps on entry.
The METV is possibly a viable visa to get (although expensive) but with the recent change that the new ผ.60 stamp is not subject to the two land border entries per calendar year rule, it certainly seems like its value is limited or not really necessary at all.
For the extension based on tourism they will add on the 30 days to your existing stamp. Depending on the office you use you can do the extension from 45-7 days prior.
No it is not like a 90 day report. Depending on the office you use you may be able to get a year extension of stay 45-30 days prior to your stamp running out. There is no grace period after it’s due.
But to answer your question, if the visa arrives after you have entered using the 60 day exempt stamp then you’d have to leave the country and re-enter to activate it.
As the clock ticks down as soon as it’s issued there isn’t really any benefit in waiting around until the full first 60 days is over (as would be for a SETV), you can activate it whenever it is convenient for you.
They are more likely to have an issue leaving the Philippines than entry to Thailand. I’m certainly not an expert on that side but see lots of posts of issues leaving.