To a degree, but I feel you're over-simplifying. Sony makes mostly third person action adventure games, with a few notable exceptions, like Gran Turismo. Microsoft make FPSs, but they also make TPS, TPRPGs, FPRPGs, Racing games, strategy games, and so on. Microsoft's "core franchises" is a comparatively diverse genre line up, while I feel that Sony's are almost exclusively third person action adventure games with open-world RPG elements. It's made them rich, but it's almost made me less interested in the line up. Sony used to make other games as well that made fall in love with PlayStation, but over time, they've basically stopped. They don't make First Person Shooters at all any more, for example, and I can't recall the last strategy game they made.
Returnal is a third person action adventure game with rogue-like elements.
Demon's Souls is a third person action adventure game in the souls-bourne style.
Spider-man is an open-world cinematic third person action adventure game.
The Last of Us is a cinematic third person action adventure game with stealth elements.
Ratchet and Clank is a third person action adventure game with platform and arcade shooter elements.
They're all different, agreed, but if, like me, you've kinda had your fill of third person action adventure games - especially those with lots of cut scenes - Sony's line up isn't all that appealing right now. Microsoft at least have something else on offer that they're happy to put some money into - perhaps because they learned their lesson after an entire generation of "Halo, Forza, Fable, Gears". If someone says "Sony needs more exclusives", I feel that's what they're talking about, rather than a pure numbers game. In terms of raw numbers, Sony's been delivering the goods since the second half of the PS3 generation. But since then, I feel that the breadth of experiences they're interested in making has slowly dwindled.