I want to report that the same happens on my Pixel 4a 5G with a multiple-profile setup. Mine does differ from the ones mentioned above in which the main profile doesn't have ANY third-party app installed (let's call it "stock" profile) and most of my time is spent in a secondary profile. Steps to reproduce:
- Login into ungoogled secondary profile A
- Use it for an undefined amount of time
- Switch to profile B with Play Services installed
- Use it for an undefined amount of time
- Switch back to profile A
Results:
Login back into profile A takes at least 3 seconds. Trying to switch Apps with the App Navigation Menu (swiping up from the bottom) takes at least 5 seconds.
Similar to what @Marila stated, the main difference between this profile and the rest is that it has IM apps installed (Signal, WA) on it. As a bonus, sometimes switching back DOES NOT result in the UI lagging, but Signal warns about an error occurring and asks me to submit an automated bug report. So yeah, I do think this is related to Instant Messaging apps or maybe the no-battery optimization somehow.
EDIT: Build UP1A.231005.007.2023102300