Would you expect evidence that isn’t anecdotal to be easily available to the public? It’s not like Google publishes a transparent public log of every act of moderation, so compiling evidence beyond a list of anecdotes is simply not possible. However, I would argue their publicly stated policies on disallowed content is enough to see the progressive bias.

To me and other moderates, and I imagine conservatives, the bias is clear. In this last year I’ve seen Google ban content relating to BLM riots, COVID (like the lab leak hypothesis), trans issues, firearms, and more. If you take an issue like whether transwomen should be allowed participation in women’s sports, enough content is taken down that what’s left as a result of Google’s censorship is a significant amplification of the views of dedicated trans activists relative to everyone else. Google doing this at their scale amounts to propaganda - after all, they are more influential than most governments given the large number of users they have.

Your definition of “well deserved” may fit your own worldview. But for me, I see a brazen suppression of free inquiry, and in many cases, the truth. These actions are framed as being positive, by defining censored content as “hateful” or “violent” or whatever, but they’re actually just damaging and dishonest, since they inhibit open discourse. It’s an important enough problem to me that I can’t support any new service that simply recreates the same oppressive mess - I just don’t see the point because whatever other features they might have, it will still feel mostly the same if this problem isn’t fixed.

I'm very doubtful as my own experience would lean strongly against it having worked at multiple similar companies (facebook, tiktok, snapchat) and having even worked on recommendation system area. Internally the typical employee tends to be liberal/libertarian and for facebook I remember conservative employees being so rare there was one person doing meetups with anyone interested to talk to an open conservative in the company. For tiktok I worked on the main team in the US about recommendation engine for videos and content like BLM was very supported and pretty frequently would appear as a hashtag in trending page.

I haven't worked at google specifically, but having heard plenty of people complain about tiktok/facebook recommendations with very incorrect guesses on what the system bias is, I'm doubtful google is biased against that type of content. Snapchat isn't known as much for recommendation so haven't heard much feedback on it's system.