Well, I'm not a doctor, and I don't even really know what the "standard timeframes" are for experiencing changes. But, I can share my experience. YMMV.

After a lifetime of consuming caffeine, early in the pandemic when I started staying home fulltime, I saw my opportunity. I'd been trying to quit both coffee and caffeinated sodas for years. I immediately noticed the withdrawal symptoms, but then I'd had them for so long: irritable and dehydrated in the mornings until I had my fix. It took me 6 months to finally ween myself off coffee in the mornings. Sodas had fallen by the wayside earlier. So I finally was caffeine-free on Oct 26, 2020.

It took a solid 4-6 weeks, likely toward the longer end for the morning cravings to really stop. After that it took me another 2-3 weeks for my restless leg stopped moving. It took about 4 months after that for my body to readjust to not constantly shaking my right leg. Parts of the musculature of my hip had over-developed in the decades I'd had that problem. I continue to work on stretching out that part of my body on an ongoing basis.

The real gains started after about 3 months. That's when I noticed I slept much more soundly. Falling asleep remains significantly easier, as does waking. I'm never irritable in the mornings unless I read some awful news first thing -- point being that the caffeine withdrawal symptoms have abated.

I think more clearly. I'm not as easily irritated. I feel like caffeine left me on an emotional raw edge, and I was always snapping at people, or much worse. It ruined my emotional state for the majority of my life, since I started drinking colas heavily around age ten, and I'm 46 at present.

It has really been a very eye-opening experience. I feel like a fog on my mind cleared after a lifetime. I'm not sure I can really relate that feeling with mere words.

TL;DR: ~3 months from cessation I started to notice real benefits