Sharing a bit of my experience in case it's of help. I live on the Blue Ridge Plateau in southern Virginia boasting some of the best agricultural conditions in Appalachia. I've lived here 18 months, and am told last year was dry. 2021 saw 56" of rain, we're just under 22" for 2022. For about 8 months of the year we have lots of fog and mist that my weather station doesn't record, but keeps the soil from drying out. I tossed excess garlic into a ravine in the woods filled with sticks expecting it to die. I now have a "strategic garlic reserve" lol. Really easy to grow stuff here!
I acquired a flock in July of adult hens and POL pullets. During the growing season, I ran 10 chickens behind 100' of fence. I have about 1 acre of cleared land which also contains the house and garden. While the chickens wouldn't strip their area to bare earth, it seemed like about a week was the best time for them to be moved. They will dig holes, sometimes surprisingly deep. Before I was catching coop poops, I'd end up with a very concentrated pile that would have to be raked. Routine was to mark and mow new fence line, move the chickens, rake their prior area, mow and toss pasture seed before a rain. It took 2 weeks to start to see recovery, and about 5 weeks before plants looked strong enough for chickens (during prime growing season).
Starting fall 2021, I thought the chickens could help clear some weedy areas the prior owners neglected, fertilize the veggie garden, and clear a new garden expansion. I tossed a winter cover crop into the existing garden and the plot that will be additional garden space. They spent 2-3 months before moving, with an additional 50-200' of fence added. The garden's soil was already soft and they performed well there. I was surprised to find a handful of Austrian peas overwintered, but not much else has come up. The other areas, the chickens did not destroy any of the root networks so everything is coming back. A whole hill full of daylilies again. *sigh*
I believe a smaller area, like a tractor, would need to be moved more frequently than once a week. I've heard of "mob grazing" from folks like Joel Salatin - give the animals what they can eat in a day and they will take a bit of everything instead of just the tastiest bits. I cannot attest to the accuracy of that concept.
It could be that if you would like chickens to more or less till, a tractor with a smaller area could be better suited. Giving them more space is very conducive to gradually improving pasture through fertilizing and/or overseeding (which is my goal, plus having coop poops for compost). However, recovery time will be severely limited during cold and dry times.
I did find some information from Justin Rhodes to be useful, but he's redone his website since last I looked. I found a blog post with some math on how long it takes chickens to "till" X square feet. His "chickshaw" is worth a look as well if you're not already set on having a tractor.
https://abundantpermaculture.com/