Something weird to consider. Right now the all these large companies are fighting for your time.
Could there be a scenario where MS GAAS become so popular on Sonys platforms it takes away from their own GAAS ambitions?
Not at all. PlayStation has a ton of popular live service games already, a few more being added to the pile doesn't alter SIEs plans. They've still got several live service games that're active and in the works with:
(active)
MLB
Helldivers 2
Destiny 2
(upcoming)
Marathon
Matter
Concord
Fairgame$
Horizon Online by Guerrilla
Horizon MMORPG by NCSoft (assuming it's separate from the above title)
There's also apparently a secret team working on a game under Jason Blundell. Whether that's also a live service game or not remains to be seen, but if they're continuing the work from the game Deviation was originally working on then that would fall under the live service banner too.
SIE has been taking steps over the past several years to widen their sources of income to be more self sufficient. That's seen them do steps like start up PS Productions, embrace premium subscriptions and hardware, put games on mobile/PC and begin the current live service push. They're looking for more revenue/profit, and that doesn't change because a few more live service games are being added to their platform.
Plus SIE is all about that synergy. They want their own IP to explode in popularity so they can push transmedia content like film/TV adaptations and whatnot, sell merch and do cross promotional content between their own IP to bring in even more DLC (skins, shaders, outfits...)