Then how come all of a sudden all of them were roped into making GAAS titles?
Surely not all of them would get sudden inspiration or creative spark to make GAAS titles. Not at the same time at the very least.
This is too much drinking of the marketing cool aid from Sony.
Not all of SIE's studios are making live service games. I think you're confusion is that SIE has decided to push for more live service games and as a result has opened up more resources to studio who want to go that route. Hermen Hulst ain't out there with a clipboard saying, "Studio A you do a live service game. Studio B you can do a single player game. Studio C you do one of each". That's not the way it works. The studio decides what they want to do, as always, and if the studio heads decide they want to do a live service game then they do their pitch to SIE and arrange for whatever resources they need. That could be funding to expand their teams, support studios, whatever.
Look at it this way. In the past, many SIE studios would tack on a smaller multiplayer mode to their games. Uncharted had a MP mode. TLOU had a MP mode. Ghost of Tsushima had a MP mode. Well now those studios are being offered additional resources to make those games into full blown live service games, if they choose to go that route. That's what this is. With TLOU2 the MP mode was growing in ambition far more than what a normal MP mode would be, just around the same time is when SIE decided to make their live service push, so they decided to spin that off and let it grow into its own fully fledged live service game. This wasn't some mandate from above that came down, this was the studio organically shifting into making a large scale live service game.
SIE is all about giving their studios choice on what they wanna do, they only offer more avenues for those studios to go in, and offer additional resources. Those avenues include single player standard games, live service games, VR games, and now the option to port their games to either PC or mobile.
As for studios with live service titles coming out, let's take a look at that. Let's check your assertation that SIE's forcing live service games on their studios. Let's start with the long standing studios before the recent acquisitions over the past few years (Note that apparently Sony and Polyphony don't consider GT7 to be a live service game):
Naughty Dog - TLOU MP
San Diego Studio - Yearly MLB live service releases
Guerrilla - Live service Horizon game
London Studios - Live service fantasy game
So 3 existing studios doing a live service game. While Naughty Dog and Guerrilla are also working on additional single player content at the same time. Does this look forced to you?
Well let's look at the studios Sony has acquired since 2019 who're doing live service or possible live service games if we're unsure:
Bungie - Continuing Destiny 2, new live service game codename Matter, and another live service game Marathon
Insomniac - We know they've been hiring for some sort of Multiplayer project, but we don't yet know if it's a separate live service game or just a MP mode for one of their other games
Haven - AAA live service project
Firesprite - They've been hiring for a multiplayer shooter, maybe Twisted Metal? Unsure if it's live service
From the above list Insomniac and Firesprite are continuing to work on multiple single player games while possibly also working on live service games. Bungie was already doing and planning to do more live service games. Haven is a brand new studio whose first project they pitched to Sony was a live service game (well, they pitched several ideas and Sony wanted them to do all of them, but Haven settled on one to start). Does this scream "we're being forced to do live service games!" to you?
How about the third parties making live service games for SIE?
Deviation Games - Brand new studio formed who pitched a live service game to SIE as their first title
Firewalk Games - Brand new studio formed to do a live service game for SIE
First Contact Games - Making Firewall Ultra for PSVR2. It's multiplayer, and many suspect it falls under the live service banner
Arrowhead Games - Leaks show they're making Helldivers 2, another live service game. The first game was a MP title, so the second becoming a live service game is a logical next step
So who's being forced from that lineup, huh? No, there's no kool-aid being drunk here. It's plain and simple facts. If SIE were in the habit of forcing their studios to work on certain projects don't you think half their studios would be churning out PSVR2 titles? The studio chooses their path and SIE supplies the resources. No one at all is being forced to make live service games.