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...
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 know google sites (especially Google search) are a much more polished experience on Chrome, but I haven't had an unusable experience on Firefox, I don't notice a problem.
I think I missed that that isn't your point. You're saying google streamlines things for people on Chromium to make it a nicer experience, making it harder to switch away. And I think you're right about that.
There are quite a few online web stores I patronize in which the shopping cart is broken, or the checkout is broken and there's no way of paying in Firefox.
My bank's online banking site is broken too in Firefox. It's okay to pay for things and display basic checking account information, but more detailed personal finance pages are unusable.
My company's ERP is half broken in Firefox.
And quite a few porn sites I download stuff off of are broken too in Firefox.
And that's with NoScript, uBlock Origin and Ghostery fully disabled.
Obviously all those sites are streamlined to work well with Chromium or Chromium-based browser because - surprise surprise - it's the most common browser type, which is exactly the position Google wanted to place itself in. It's was very same problem when websites were designed to work primarily with Explorer, when Microsoft dominated the browser space many years ago.
This is not my experience. For the sites I frequent, though Firefox is generally not listed as a supported browser anymore, the sites work fine. That includes banking and any random shopping cart site. That's probably because in my country there are common payment portals, and for you the common payment portals are probably different.
One site I have trouble with is one for health insurance, but a user agent spoofed to look like Chrome makes the site work fine (I hate so much that they do this, and have complained but I'm just one customer).
I wonder what happens if you spoof your user agent. It's probably a deeper issue, but might be worth a try.