Mostly the latter.

It's somewhat perceptible. The worst, for me, is the search for apps, which visibly lags. My battery has been replaced and shows 99% capacity. This is an iphone 7 with the latest ios upgrade it can get, 15.6.something IIRC.

I think another issue is that apps do tend to get more sluggish, since they probably expect to be running on newer hardware. If you stick to an older ios version, if they're deemed incompatible, they won't update. But as soon as you're on the latest ios, you get the app updates, too, if you've left the default on.

Google maps, for example, is clearly more sluggish than before. Apple maps is practically unusable. Youtube crashes reliably (but works fine in the browser...)

I had a 3rd generation iPad which became borderline unusable after updating to iOS 7 or something like that (they added the custom keyboard function then and after that update the onscreen keyboard took seconds to appear) That was before the battery went bad.

I think there is a psychological aspect here as well due to confirmation bias — all caches will be wiped during an update so even due to that the first few hours/days may be slightly slower. If people make this assumption they can later easily find evidence for that (or its negative as well, if they would try to look for that)