Since he's been there, he's been happily just burrowing around in the dirt and (probably) eating some bugs. He's totally welcome to stay as long as he wants, I think he's pretty neat. My concern is, I read skinks aren't that great at climbing, unlike geckos. If he wanted to leave the bucket, would he be able to? Or do I need to catch him and set him free?
I think it needs some help getting out of there,maybe you can put some thing in there for it to climb on.
They do an important job eating bugs and snails protecting your tomato plant(s).
Try not to use any pestecides where it lives.
It is best if you try to avoid catching him it can have a negative effect on him some of them are known to drop their tail if they get scared.I do not know the exact type you have there https://en.wikipedia.org/wiki/Skink