The first amendment protects citizen speech from the government. It does not protect speech from consequences or actions by private individuals or companies.
And free speech does not begin and end at the first amendment. A company can violate your ability to speak freely without also violating your first amendment rights.
Freedom of speech is infact dead. When the government and corporations are in bed with each other, that's a convenient way to separate actions. And as we've seen in so many other ways, the government loves to use corporations to do the things that they "aren't allowed" to do, because tech moves at light speed compared to laws
It seems like you understand that your argument does more to hurt your point than help it. That story is exactly why people say ACAB because even the "good ones" eventually get broken down by the system (assuming they don't get terminated or end up getting shot somehow during duty) and end up going along with it.