Because of the amount of freelance work I do around town, I made a PowerGrades folder that I throw on a thumbdrive and take along with me (assuming I can get USB access to the client computer). I can always restore these in a few minutes whenever I create a new Project Database.
I export each PowerGrade folder to its own similarly-named folder, and I also create an embedded graphic for each PowerGrade (and a label) so I can see at a glance what I have. Make sure you name each Gallery Still and also Name Each Node when you create the Powergrade. From inside the new Resolve system (or on another database), I create a new Powergrade folder and label it accordingly. Then I switch to "1 Still Per Scene" and import just the DRX files, which also brings along the associated still frame.

I have hundreds and hundreds of them (looks and fixes and node setups, oh my), so it helps to stay organized and have different folders for different looks or different projects (or different effects). Be aware that you can't move Powergrades -- or grades of any kind -- from 20 back to 19. You can always go up a version, but never down.
I don't know of a way to move or copy Powergrades within the Gallery database itself, but I'm all ears if somebody has a method.