Oh, the lag thing.... based on everything that I've pieced together, I think I know what is going on. There's a bunch of steps involved with installing an over-the-air update like this. If you let the phone do it, it'll download the file and when it installs, it fires off a bunch of scripts to load the update on the the the inactive system partition (remember, the Pixel 2 has two of them)... it then runs a bunch of stuff to pre-load it, then it will boot into that second partition without the need to go through the old "Upgrading Android" recovery screen.
The phone will then boot up and run a few cleanup tasks to finish things up (That's that notification you see).
Now, I don't think that this lag has anything to do with that notification... that's been there all along. I think whatever is causing this is a difference between how the phone installs the OTA on the secondary partition when fully booted vs while in Recovery. They might have tweaked something in all those preload scripts and whatever it is isn't getting called properly when you load the OTA from Recovery...
But when you reboot the phone that last time when its laggy... somewhere in there, that function gets called (maybe it's something to do with the runtimes, that's my guess) and everything starts running as expected.
As someone who's been in QA for way too long, my money is that whatever is causing this doesn't occur in every phone that sideloads the OTA...and I am positive they spent FAR more time testing the OTA install from the main system menu because that's where 99% of the users will kick it off. So.... the tests of the Recovery OTA probably passed the few times they ran it and they never saw any issues on boot so they marked it passed and moved on to the next test case.