I consider myself virtually spanked for bumping a thread with the same title as this to page 1 :)
According to the annotated solutions FRISBEE is Fri's (Friday is) Bee (busy)! I thought FR as an abbrev of Friday was a bit lame.
They also confirmed TWIRLY as expected, they didn't say whether SWIRLY would also be acceptable, so the green tick mystery is unsolved.
And they say PUPPET is a software tool? I've not heard of that and I am a programmer ;) Maybe some of the animators use one of those, but I would call it a marionette instead?
Typical Graun though, they got the number of the puzzle wrong in the page title
https://www.theguardian.com/crosswords/2021/nov/07/annotated-solutions-for-prize-28584