As far as I'm aware of, I've not seen any native function that can accomplish this, and discussing 3rd party applications will arguably constitute as a request for software recommendations, which is against community guidelines here.
However, since I'm here, I may as well take a shot at pointing you in the right direction, I'll leave it to the more senior members to decide on whether to flag the OP or not.
For "full screen capturing" I'm aware there are several solutions, including one for Chrome which saves directly to G Drive. This is the only noteworthy extension that I will mention simply because it's the only one that's arguably trustworthy, as it's developed and published by the official Google Drive dev team.
For desktop environment, what I would instead use (until an easier and reputable solution comes forth) would be a utility that enables you to append images quickly, and can be actionable with automation. I personally would use something like ImageMagick, in combination with AHK.
Note: AHK likely has the capability to accomplish the desired function on it's own, but I've not seen any showcased script for it, and it'd likely not be a viable route to attempt to write it yourself if you aren't already familiar with it.