I use Firefox and Firefox Mobile on the desktop and Android respectively, Chromium with Bromite patches on Android, and infrequently Brave on the desktop to get to sites that only work properly with Chromium (more and more often - another whole separate can of worms too, this...) And I always pay attention to disable google.com and gstatic.com in NoScript and uBlock Origin whenever possible.
I noticed something quite striking: when I hit sites that use those hateful captchas from Google - aka "reCAPTCHA" that I know are from Google because they force me to temporarily reenable google.com and gstatic.com - statistically, Google quite consistently marks the captcha as passed with the green checkmark without even asking me to identify fire hydrants or bicycles once, or perhaps once but the test passes even if I purposedly don't select certain images, and almost never serves me those especially heinous "rolling captchas" that keep coming up with more and more images to identify or not as you click on them until it apparently has annoyed you enough and lets you through.
When I use Firefox however, the captchas never pass without at least one test, sometimes several in a row, and very often rolling captchas. And if I purposedly don't select certain images for the sake of experimentation, the captchas keep on coming and coming and coming forever - and if I keep doing it long enough, they plain never stop and the site become impossible to access.
Only with Firefox. Never with Chromium-based browsers.
I've been experimenting with this informally for months now and it's quite clear to me that Google has a dark pattern in place with its reCAPTCHA system to make Chrome and Chromium-based browsers the path of least resistance.
It's really disgusting...
It's not necessary targeted like that. Remember Chrome sends a lot of information about the user, allowing them to more easily gauge if it's a bot. Firefox hides a lot of information, blocks a lot of third party scripts by default, and even sends fake information for some things. For all intents and purposes, Firefox looks much more like a bot than Chrome.
With that said, I use Firefox exclusively and don't have anywhere near as many issues as you seem to.
Remember, I use the equivalent of Bromite on Android and Brave on the desktop. Those are not Chrome: they're heavily privacy enhanced. By your theory, those browsers too should serve you more annoying reCAPTCHA more often, just like Firefox. But they don't: even on those privacy-respecting Chromium forks, you can get past reCAPTCHA much easier.
Try using Chromium side by side and the subtle extra difficulties of sailing through the Googlespace become quite apparent. As long as you stick to Firefox, you don't realize that the Chromium experience is ever-so-slightly slicker on many websites.
I wonder what happens if you spoof your user agent. It's probably a deeper issue, but might be worth a try.