Could you in theory sue Google for (intentionally or not) discriminating against you in the search results? Just in theory.
IANAL but I doubt they'd get very far. What would their actual argument even be? Google isn't obligated to include every web site in existence in their index.
I believe in this case protonmail was hit by an algorithm based derank (not a manual action). What causes it is anyone's guess. But something series of events hurt their ranking. Its also important to note that PM was NOT delisted. They still were getting traffic from Google, they were just deranked.
No, but to have a competing product appear highly ranked at first, then drop off their search engine entirely and not return until there is a public outcry, screams of anti-competitive action on Google's part[1]. That said, I don't think a lawsuit would get very far either. I'm just saying the whole affair is fishy.
[1] Or, if you want to go tin-foil-hat with it, perhaps a certain government told Google it didn't want people to know about a secure email startup that resides in a country that is known for upholding privacy rights. I don't buy that one myself but I've seen it bandied about in the past in similar cases.
Or Google might be broken up – there’s also antitrust cases against them in the US.
With more than half of the population using them, and them holding > 90% in multiple such markets, they fall into the category of monopoly that automatically becomes a public utility – they’re supposed to be just a dumb pipe.
Defusing a court case would seem helpful. Explaining to those worried by this might be good.
Acknowledging you screwed up, fixing it and publicly stating you will do better (then doing better) can actually boost the way a company is seen.