base model PS5 does not have built in FSR of any sort

Well nobody has built-in FSR. It's a software that runs on the GPU. (With the relevant exception of PSSR). The reason FSR4 only officially supports RDNA4 and up is because RDNA4 has much faster 8-bit floating point operations. Floating point operations is the primary thing GPUs are used for. So it's a very general improvement/design change/new feature that allows FSR4 to run fast, not a specialised extra chip in RDNA4 series GPUs. 8 bit is very imprecise and therefore less used in graphics, but good for AI. Nvidia already had this.

studios can write their own implementation of FSR and there’s apparently a few games that did just that, but the majority of PS5 games don’t

So FSR is a specific program using a specific algorithm. (With FSR1, 2, 3, etc being different from each other). So nobody is writing new FSR implementations. Might not even be legal. It's a case of including the program (and of course writing the surrounding code to use it, which is probably what you meant). But I mention to highlight that the reason most PS5 games don't use FSR is because FSR usually wasn't the best use of that performance.

(FSR1, and to some extent FSR2/3 worked on very sparse data, they're essentially post-process effects. If you're writing a game engine then you have a lot of insight into the frame and can instead use similar tricks to upscale along the way, or with using data from previous frames, data from non-final passes, etc, to upscale your game either cheaper or better. For example Epic's TSR is able to get better results for cheaper because it's more integrated into the steps along the way to the final image. There's also XeSS which looks better and supports RDNA2 at least on PC).

You didn't see much FSR1 use because it wasn't very good. I'd think 2 and 3 are more popular. And on the previous topic of hardware requirements: Steam Machine is RDNA3 so it's FSR3 they're talking about for the Steam Machine - Same one the base PS5's RDNA2 GPU can use. So I can't see it being any sort of silver bullet - But it is true that RDNA3 has some new features over RDNA2. If a game is built around intense matrix maths it can't run on PS5 but can on RDNA3. There will be some shaders and AI-adjacent things that run faster on Steam Machine. But not FSR.

custom co-developed implementationPSSR, a custom implementation of AMD’s FSR that they co-developed with AMD

It isn't, it's it's own thing. Or rather, it's FSR4, not FSR1-3. FSR4 and PSSR are AI, that means they need training data. And that's why PSSR is made by/with Sony, because Sony is allowed to use PlayStation licensed games to get the training data and AMD isn't. Unless Valve has done something clever with the license they aren't allowed to train on Steam games. (Of course the way Nvidia got around this was to just train on commercial games and not worry about it, so maybe PlayStations' catalogue isn't actually that valuable =P). So it's unlikely that the Steam Machine will have a proprietary FSR4 model that's better than the AMD provided one.

I think the reason Valve's messaging has been so heavy on FSR isn't because they have a way to make FSR better cooking in their lab, but because they want to be able to simultaneously say "4K" to console players and "Not 4K" to PC players. Hence "4K with FSR".

I hope this is clear and not too wordy and not condescending. It sounded like you were misunderstanding FSR slightly.

they were primarily making noise about Frame Generation

Some people don't like frame generation because it adds latency and works poorly with V-Sync. But there are also a lot of people who just hate AI because of how it's made. You see it every day on Lemmy.

I’m of the opinion that the Steam Machine will easily match the base PS5, and likely land somewhere between it and the PS5 Pro

I just don't see how that's possible without a faster GPU.

the work Valve has put into Steam OS itself and how it may compare to running the same games under Windows

It's true that sometimes the same Windows game can run faster. But in this case we're talking about GPU-limited games, and there the fact that Linux is faster doesn't help. Both on Linux and Windows the OS overhead is negligible and the GPU driver is in complete control. If a game is ever faster on GPU side on Linux it'll be because the emulation was bad and skipped some steps.

I’m not some hardcore Valve fanboy and am open to new information/perspective changing my opinion. I appreciate the discussion :)

I didn't get any sort of bad impression. I don't think anything you said is unfair, but I'm making the case for why I disagree.