The ecosystem works a little differently than this description implies.
For chromium/google and firefox/mozilla, the vast (vast!) majority of revenue supporting the development efforts comes to the parent companies via searches you perform. The browser itself is incidental to this model, and the browser does not do anything unpleasant or unexpected other than follow standards, which themselves allow for tracking and other activities by ecosystem participants to facilitate the delivery of advertising.
There is out of band communication between browsers and their parent cloud services but it is in service of safety- retrieving lists of compromised sites, revoked certificates, pinned certificates, etc.
The browsers do not communicate site visit data directly to their clouds without your permission. Instead, google relies on publishers near ubiquitous use of google analytics to associate visit data with a cookie.
The integration of analytics and advertising on publisher sites directly is the far more problematic machinery. It is this machinery that is targeted by Ad Blockers.
So the browsers themselves can be used safely, but ANY browsing- even using text browsers- triggers activities that you may be concerned about.
In terms of answering the specific questions-
There are a ton of browsers at different levels of maturity and with different postures when it comes to privacy. Very few can be considered serious. A browser is a huge, huge engineering effort these days, as complex as an operating system. Long gone are the times when a single person or even small team can produce something meeting even basic levels of capability.
Big teams need funding, and funding a big effort without sponsorship dollars, like those from advertising, is a nut that has not been cracked.
An ostensibly serious recent entry, with a bitcoin-integrated revenue model, is Brave:
In terms of the chromium and mozilla codebases, they both have a huge amount of oversight and testing. Their core code is not a candidate for injected compromises. However, plugins for both are far less well policed and monitored and have been abuse vectors in the past. Be very very careful when installing plugins, especially ad blockers and others that purport to protect privacy. Some do the opposite.