In the old days it used to be called "riding the board"-adjusting the faders and settings of the mixing desk WHILE playback was happening, to get more organic results instead of using the same setting for the entire mix.

But I dont know how to phrase this question to ask how to do it with a modern DAW (I use Cubase)-and trying to find anything with search engines is impossible lately.

So-how do I "play" a plugin, live into the mix so that my "playing" those settings gets saved so it will replicate and play them back after?

In this instance, with a stereo placement plugin?

TLDR-How do I get Cubase to save me "Playing and live adjusting" plugin use?

Set the track to write [W] and leave it on read [R] when you are ready.
It's called automation.