But does it? When you have platforms running the same CPU and GPU arch with a good API should it really make that much of a difference?
This isn't PS2 vs OG Xbox era where PS2 was so backwards.
Yes, it can still make a huge difference.
E.g. the API can handle "commands" differently. Just as an example: DX11 commands tend to do more than is necessary. They make things for memory management, to automatically dispose unused memory, log many things that might be used, ....
This can make a huge overhead if you have designed your engine for "one call to get it all" but than the "requested design" shifts to many, many small calls instead. Now the small overhead you had with each call (but made things in the end much easier) get to a point where this overhead is really huge. It is not only memory but also cpu-/gpu-usage that are affected by this.
This was basically the shift from DX9 to DX10 to DX11 to finally DX12 (which is more or less, just do it yourself). And still many engines for games are DX11 based and do not really translate good to DX12 on PCs. Yes the API of the xbox is a little bit different but still has the same issues, as it lets developers decide what they want to use. The "old" way is much easier to get things done, but not the most efficient way. To use "almost" the same API for PC & xbox is very attractive for developers. Easy to port and get it to run quite fast. In the optimal case, now it would be good to optimize the calls for the system, but as everything more or less works "fine enough" more optimizations are not needed to ship a product. On PS4/5 you don't have these "issues". The developer must translate the commands to Sonys API. There is "nothing" compatible. So in this process (s)he already optimizes the code for the system (if (s)he wants it or not). Also not every command can be translated 1:1 which also leads to more optimal code, because the developer must do something.
Btw, we can often still see this in games, where the PS4 is in front of the xbox one in CPU limited scenes, even though the xbox has the (a bit) stronger CPU so it should always be in front in cpu-limited scenes. But the API makes the difference here.