I'm a lifelong Nikon guy, but don't have any experience with the new FF Z series.... I've brought along DSLRs (in backpacks) a few times on the bike, but more frequently I have used my little Nikon "1" mirrorless camera.... It fits just right in my little underseat bag. Sure, it's an orphaned system, and big fast ultrawides and tilt-shift lenses don't exist for it (but you could use them, I suppose, with an adapter, which would take up more space in your bag).but the resulting pictures from it are amazingly good. I wouldn't pixel-peek them side-by-side with a good FF or even a DX format DSLR, but considering the tiny size of the camera, they're more than good enough for my needs.
I also have a Sony A6000 mirrorless, but don't use it often because its battery life isn't very good. My Nikons can sit in the bag all week and only lose a percent or two of charge, but the Sony will lose 60-80 percent in a week whether I use it or not. If I shoot with it on a Saturday, I MUST charge the battery again if I want to shoot with it again on Sunday.