As deplatformed people and groups migrate elsewhere, they may lose followers but also become more hateful and toxic.

No, what happens is that these groups self censor on the mainstream platform in an attempt to avoid getting nuked. It never works because those platforms are run by pedophiles who are playing bad faith games. Then they make their own site where the pedophile admins aren't a concern so there's no more censorship. The reason this place is an exception to that rule is that we made the mistake of importing our faggot janny from the pedo site.

Meanwhile, warning labels seem to work less effectively for fake posts if they are right-leaning.

They only label right wing posts, and they do it without regard to the truth. It's not like they fact check leftists, so there's nothing for them to study on the other side of the political divide. But it's good that people are seeing these "warning" labels for the political hit jobs they are.

But this would also need a coordinated effort from mainstream platforms as well other media to work.

Like when they conspired against Alex Jones to prove that there's totally no conspiracy?