We've had many, many discussions on vermicomposting here, although I doubt that we've said everything there is to say! There's always more to learn.
One of the threads is [url=https://www.helpfulgardener.com/forum/viewtopic.php?p=178711#178711]here[/url], and it contains links to other threads. I also just performed a Search of the Forum (up in the lime green words near the top of the page) on the phrase "vermicomposting" and got about 150 hits--not threads, but posts--so there's a lot out there, some of it written by me, some of it by people with more experience. (I only have three years of experience this go-round; I had two or three years previously, but the worms met a sad fate.
On your original question, I usually move the worms around very gently with a trowel or hand fork. I've probably touched them the least of anyone here, since I have a very strong "yuck" factor for wiggly sensations on my skin.
(I know, everyone, I know: these hard-working invertebrates are creating excellent soil amendment on my behalf, and I feed them and shelter them so they can do just that. However....)
I was fortunate enough to purchase a discounted Worm Factory from the county; I don't know whether subsidies are still available in this day of cutbacks, but the overall goal of reducing solid waste is long-range cost-effective, so it's worth looking into.
Sunset Zone 17, USDA Zone 9