If I'm playing modern games on a TV? PS5 easy. But still the pro over the deck.
I love my deck. As the handheld it's intended to be. It's not powerful enough for an acceptable experience running a AAA 3D game on a TV screen. You can ignore the resolution and artifacts and just generally low visual quality and poor frame rate on a small screen, because playing the games portably at all is a huge step up. You can't ignore any part of it on a TV. It's fine for indie games, older games, 2D stuff, etc.
But it doesn't have the performance for a good living room experience if you're looking to play modern AAA games. (Ignoring all their bullshit rootkits on PC that block a lot of multiplayer games out completely, which are the games you have to pay for on PS. You just can't play most of them on Linux at all.)
Yup. As someone who hasn't had a dedicated gaming PC in about a decade, I've been really happy with the PS5 + Steam Deck combo (well, plus Switch, but that thing collects dust until Nintendo releases a Mario platformer).
I recently got a laptop that's not made for gaming specifically, but can handle them pretty well (with Proton), and that has scratched any itch I've had for PC games that don't lend themselves to Deck or console (your RTS games and such).
At risk of giving away the game... I think people would be very surprised to see how cheap physical copies of PS4 and PS5 games go for when you catch them on sale.
I love my Steam deck, and bounce between how heavily I use it vs the switch* or PS5 depending on the games I'm into at the moment. But misrepresenting its utility as a modern living room PC (like the OP) doesn't help anyone and is just going to leave people disappointed.
The PS5 is probably my smallest library (and mostly PS4 games, a lot of which were before I had a PC), but it's definitely plenty capable and I don't regret the purchase at all. (The controller is also the coolest non graphics addition to gaming I've experienced in a long time).
*The switch desperately needs a 3rd party replacement for the controllers, though, because the joycons are bad brand new.
That, and monitor/TV size increased a lot at the time when flat panels became a thing, so you need a higher resolution just to achieve the same pixel density you already had on a smaller screen.