Sounds like Pro you were testing was faulty or something in the settings / OS. I have never seen my MBP 14" Base lagging in anything, no lag in web site loading or app switching, all happens instantly.The lag is when loading up a webpage. Sometimes using the mail application and other applications where you are loading content. This is where the M2 air was noticeably faster. Webpages load almost instantly with the air. While the M1 MBP 16“ M1 max would not.
Again I am not saying the M1 was slow but when you buy a very expensive and supposedly pro laptop you expect everything to be instantaneous. Maybe that is a little unrealistic but that was my expectation.
When using the M2 everything is pretty much instantaneous including app switching.
I definitely find the M2 air to be faster while browsing but I don’t ever have more than 5 or so tabs. The M1 Max with 32 gb ram was slower in browsing than my M2 air with 16gb ram. Now neither is slow so let’s make sure that is stated.
Regarding settings, I have noticed that using Monterey hide my ip functions, causes obvious lag sometimes but that is more due to lags coming from this additional routing this function causes, and likely it may differ depending on which country you live in. I remember when this function first come, it did not work for me at all, nothing was loading in any of my Apple gear. Just recently tested it again, and it works now but there is this lag sometimes from this. But without this never any lag in MBP for me. Also some ad blocker might cause delays as well as browser plug ins.