My personal opinion is to not use anything Chrome/Chromium based (Especially that Chinese owned Spyware, Opera Browser). Reason being, it is owned/controlled by Google. Some of those web sites which you may be having issues is because over 90% of browser usage is on Chromium based browsers. Do you really want to give Google that much power over the web?
Some will say “but muh open source!” The problem with that idea is while, yes it can be forked, the issue comes up when Google pushes a change. Those Chromium forks still have to identify themselves as Chromium. So when Google pushes a change on Chromium, the web site developers will adapt to that change. If the forks do not follow, their browsers will either start to show broken sites, or saying they do not support their browser.
Switching over will just make things worse. If you got a problem with a site, complain to the webmaster, or the company.
My advice would to be use forks of Firefox. Reason being is Mozilla has started politicizing their add-on store.
It’s not the engine itself. The problem with forked browsers is they have to follow the changes of the source. If they don’t they can become broken. In this case Google controls it. The site developers will of course follow, and use those changes which come from Google
Chromium based browsers have well over 90% of market share. I am not sure why people keep using those, giving so much control over the web to Google.
I don’t know about purposefully in some cases but I know Google has done that for sure on things like Google Docs where they arbitrarily break things in Firefox that work in Chrome/ium.
I work on websites so I have to test in multiple browsers but my secondary for personal use in the case of a fallback like you are asking about is KDE Falkon. Falkon technically uses some pieces from Chromium but not the full stack so it isn’t exactly the same but ultimately it does help the chromium engine. This is why I almost always use Firefox but occasionally Falkon.
As for Yandex, I have no idea. I’ve never used it but if it is based on Chromium, I see no point in it any more than the other Chromium based clones.
I use Facebook exclusively through Firefox so I can use the Facebook Container addon and it is amazing. Though a browser specifically for it to isolate is another option. I am only saying that I use Firefox with FB just fine . . . although with that said, I rarely actually use FB so maybe my experience is too skewed in that sense.
I agree with this as Google has enough power in our world as it is . . . helping them amass more to the point of total dominance of the web? Firefox for me almost always . . . and by almost I mean 99.999999% of the time, I rarely use anything else but can’t say never.