Earlier quoted context omitted.
Wanting to improve their news algorithm to favor more trustworthy sources is not a violation of free speech. "Free speech" guarantees you the right to say what you want, as long as it doesn't interfere with others' freedoms (i.e., making death threats or yelling "fire" in a crowded movie theater) "Free speech" does not guarantee you a platform for your protected free speech. I have the right to claim blatantly false…
The first amendment does not prevent Google (or any other company) from restricting speech. That is a very low bar. The distinction between government and private groups is not a clean as you might think. At a large enough scale, private groups can start to take on a role in society that resembles that of a government, should we not then expect them to be held to a standard that resembles that we expect of government…
The idea is that speech should be tolerated even if you disagree with it, and that societies that make room for controversial speech are better off, in the long run, than societies that do not. As a corollary, it espouses the view that individuals should be free to speak their mind and should be tolerated even if their speech is controversial. Because we cherish Free Speech, we created the first amendment. The first amendment is not the sum total of free speech, nor is free speech merely a governmental issue. For example, the California labor protections that protect employees from being fired for what they say in their private time is an example of the principle of free speech at work, and has nothing to do with the first amendment.
The principle of free speech is why there are many processes, both private and public, in which the public is invited for individuals to air their views, whether they be question and answer sessions in companies, or local government hearings. It's also the principle behind movements to build public libraries that stock controversial books. Almost every institution, whether public or private, tries to give some room for dissenting speech in its operations and tries to create a space for people to air their views. Thus the attacks on these spaces, even if they are not attacks on the first amendment, are of concern to those of us who value free speech. This includes opposition to efforts at censorship, both public and private, whether these be the circulation of blacklists of communists during the cold war, or any other kind of punishment, both public and private, merely for speech.
You may not agree with these values, but merely saying "well, the first amendment doesn't prohibit it, so it's not an attack on free speech" is a wild misunderstanding of what free speech is.