I don't see how these laws wouldn't make your identity public to someone, even if it's not the public at large. But it'd be enough for that someone to be an individual or entity who turns out to be interested in silencing your voice. Their knowledge of your identity would probably give them power to silence you not only on their platform but also on other platforms, if access to those other platforms is also tied to one single identity.
Bots are a problem but I suspect there are other ways of dealing with them, ways that don't involve making anonymity or pseudonymity impossible.