It depends on how much organic matter you have incorporated into your soil. If there is enough, they will stay. But, if you live in an area where winters are freezing, the worms will freeze in winter. However, they will populate the soil with cocoons which will hatch out in spring.

I have been poking through older posts and don't see much about people using a wire mesh screen (or something similar) to sift the worms apart from the castings.

Other than the worms likely not enjoying this process much is there any other reason this doesn't seem popular in this forum? I've seen videos on Youtube where worm farms have machines to do this sort of screening on a larger scale to separate worms.

I'm new to vermicomposting and have not yet harvested a batch of castings yet. I was originally thinking of making some sort of hand sifter out of an appropriate sized wire mesh to pull out worms and partially composted items but am curious as to why so many post about other more time consuming methods. My thinking was that once I sifted out the worms and bigger chunks of uncomposted material, I could spread out the finer compost over a plastic sheet and pull out any cocoons.

If there's something detrimental to worm health related to sifting them through wire mesh I don't have a problem getting my hands dirty. I'm just pretty sure my wife would not appreciate me spending 2 hours with my worms in the evenings nor would she be happy if I had a bucket of unsorted compost in my lap in the family room sorting out worms while we watch a movie together. She's kinda funny that way.

Actually, I use that very thing. I have a wooden frame built that fits on the top of a large tote. I dump in the vermicompost, shake vigorously, and dump what doesn't go through back into the working bin. I do let my finished compost sit for awhile and pick out the worms as they hatch, though.
If you want to use this method - be sure to get 1/4 inch hardware cloth. 1/2 inch is to big.

I harvest by laying burlap over the new bin. I scoop vc and worms out of the old bin, spreading it over the burlap. The worms crawl thru the burlap away from the light, into their new home.
The vermicompost is then scooped up and put into a pail or extra bin. Repeat till it's done. This is very easy for me and my preferred method of harvesting.