COSMIC Screenshot only allows saving images to ~/Documents or ~/Pictures :

Customizing the location has been requested at pop-os/cosmic-screenshot@github.com#15 a year ago, but isn’t becoming a thing yet.

However, in the meantime, there is a workaround :

#!/bin/bash

MONITOR_DIR="$HOME/Pictures"

DEST_DIR="$HOME/Pictures/Screenshots/"

PATTERN="Screenshot_*.png"

inotifywait -m -e create -e moved_to --format "%f" "$MONITOR_DIR" | while read FILE
do
   if [[ "$FILE" == $PATTERN ]]
   then
       mv "$MONITOR_DIR/$FILE" "$DEST_DIR/"
   fi
done

Run this at startup (for example using @reboot bash /path/to/move_screenshots.sh in crontab) and your screenshots will now be systematically moved instantly to the right place.

Fun fact : the abovementioned Bash code was AI-generated (at chat.mistral.ai).