So what's the point of the firmware update then?
I'll preface here that 'firmware' term no longer has the same meaning it used to (especially in PS3 era and before) when these were specifically payloads written into onboard EEPRom or equivalent.
Nowadays these updates are (mostly) stored on internal SSD/HDDs not unlike any other software, so it's really just
System Software updates (there's still some things that sit inside chips - but it's not the bulk of it).
Which is what incidentally - Sony calls it. It's
only the internet plebs that insist on calling it 'firmware' as we apparently all have elephantian memories and are unable to change with the times as things evolve - yes even the GenZ-ers.
</rant>
That said - when Sony makes a particular software component part of a system-update, that means it's been sufficiently tested/validated/stabilised that it is made available to
every machine & developer out there to do as they see fit. So QA process is quite extensive and rigorous, especially for things that automatically change behaviour of the consoles. But it does
not preclude offering the same software component directly to a game-developer (or maybe a 1st party uses it before it's in the system) if the said developer is willing to take some of the risks using a less field-tested piece of software at their own cost.
That's what happened with aforementioned PSP releases (and some other things in PS4 and PS3 era), and could ostensibly also happen with a possible 'future' PSSR revision. Something as big and impactful as a RE-release (see what I did there Capcom?

) would be a great candidate to get field-testing exposure to a new iteration of the algorithm
BEFORE it's made broadly available in a system update, so getting more controlled testing, but also generate product hype if the quality is a big step forward without waiting for the System Software update schedule.
I should note here that above is still speculative as we don't know if PSSR is even used by the new RE title - but it's absolutely possible (and has been done before, as I note).