1) chromium is used by several other browsers: Edge, Brave, Opera, and probably a whole range of niche browsers I don't know about. Most of these, probably don't rely on Google provided services (I imagine that would create some funny legal issues). None of these browsers are mentioned in the article.
2) The APIs mentioned aren't exactly rocket science and perfectly good OSS implementations (e.g. provided by Mozilla) exist. Also, you could use extensions. For example, Bitwarden integrates nicely into chrome and largely removes the need for built in password managers. I think browser sync is perhaps the hardest of these. But even that should not be too hard to improvise. Cross browser sync would actually be a nice thing to have.
3) Firefox is there, it's being maintained, and you can use it. Many people do. Blanket stating that that is not an option is kind of weird. It's a fine browser. It doesn't have this problem. Chromium is also still a fine browser; and it supports extensions as mentioned before.
4) Forking/patching chromium is always an option. I think some linux distributions already do this in the same way that they also patch Firefox (Iceweasel).