I'm a big proponent of free speech, and have read a bit on the arguments against Big Tech censorship. One of the arguments against Google being able to selectively censor political content, despite being a private company, is that they could be classified as an essential service. I'm obviously getting information from sources opposed to Google's censorship, so I don't know if the wider legal community agrees with that view, but it's worth considering.
Another argument is that they have legal protections as content providers. However, the same protections don't apply to content publishers. If their censorship places them in the publisher category, they could open themselves to lawsuits. YouTube is an example that usually comes up. If a user uploads an illegal video, YouTube has protections against lawsuits. As a publisher, they would have more liability for the content they host.
If news providers and other knowledge providers are allowed to curate what data they present then I don't think it's reasonable to demand that Google be held to a higher standard. Further, literally nothing is stopping you from creating your own knowledge aggregator if you feel that Google is doing a bad job of displaying pertinent data.