> People that care deeply about free-speech tend to want a level playing ground for every person in a discussion, and to not have platforms that have a centralised bias for or against different messages or identities.

By that argument free-speech advocates would support the inclusion of intelligent design and flat earth into public schools. You seem to be constructing a strawman.

Freedom of speech does not exclude the possibility of explicitly labeling certain speech as wrong, and what twitter is doing here is definitely better that removing tweets outright.

It would be even better to explicitly include opposite sources when marking disinformation. The primary concern is that this "labeling" is just a prelude to removal.

> Free-speech is mainly about avoiding situations in which there is an authoritarian bias towards the speech of one group over another.

Allowing a heavily annotated of speech is a minimum guarantee of "freedom", and vastly better than outright suppression.