I have an old steel cross bike transformed into a grocery getter that’s outfitted with wide slick tires, a rear rack, and pannier bags that I use when I need to haul stuff around. I have a gravel bike with disc brakes, wide knobby tires, and a slightly more relaxed geometry for riding/exploring on gravel/dirt or rougher paved roads. I have a carbon “race” bike with deep section wheels and a pretty aggressive geometry for going fast on paved roads.
I sometimes get close to the “zen” feeling that I got when running ultra distances but it goes away pretty quickly when I’m doing anything but going in a straight line on flat roads with no traffic. As you can imagine this doesn’t happen often. Contrast that with trail running (most of what I did for ultras) where I was just rambling along in nature. It was much easier to look inward when running on the trails.
I sometimes ride a bike with fatter tyres in the city and I never get in that zen state. Probably because I have to stay very alert, even when riding on bike paths separate from the street.
I hate to reduce your post to tech talk. But, what bike are your riding? I try and build a lot I'd bikes and the experience differs wildly. For starters, <40 mm tires sucks for zen riding.