MacBook Pro randomly discharges from 100% to ~90% when plugged
This is normal behavior.
The key to your question is your estimation:

After some time, when it gets to 88-92%

That is right at the line (93%) where Apple estimates that charging will appear to stop.  A couple of percentage points is well within the margin of error and it's safe to say it wasn't a scientific observation you were making.
From Apple Support: About Mac notebook batteries

My battery won't charge to 100%
Occasionally, the battery might not show a full charge (100%) in macOS, even after the power adapter has been connected for an extended period of time. The battery might appear to stop charging between 93 percent and 99 percent. This behavior is normal and will help to prolong the overall life of the battery.

The thing is, depending on use, it may go a little lower than 93%.  Most things done with battery is done based on calculation of what's measured so 93% is a calculation.  The point is, a hard 93% would not be that the demarcation of when to start charging.  Like everything else, it is based on the measurement; and in this case, most likely the measurement of the remaining charge and max charge values read directly from the battery itself and not a calculation displayed by the OS.
Regarding Catalina
Catalina introduced a Battery Health Management feature  and released it to the public June 1st 2020 in the 10.15.5 Update.  The Support article I sourced the info from above is from May 26th, 2020 (Pre-Catalina, see image below).

Apple has a habit of not dating things or just showing you when things were updated so, took a screen grab for posterity
It's also been in the public beta for some time judging by the ample blogs/articles written about it.  Now, it wouldn't be uncommon for Apple to implement a portion of the the feature (like changing the max charging limit) into earlier versions of macOS.  The full &quot;Battery Management&quot; feature allows you the ability to control it.