A cursory look at the raw VAERS data from the CDC[1] shows:
Reports of adverse events to VAERS following vaccination, including deaths, do not necessarily mean that a vaccine caused a health problem. (...) During this time, VAERS received 10,688 reports of death (0.0022%) among people who received a COVID-19 vaccine. CDC and FDA clinicians review reports of death to VAERS including death certificates, autopsy, and medical records.
In contrast, the CDC[2] estimates that 817k people have died of Covid-19 in the US which puts the mortality at 248 deaths per 100k individuals. Currently, an unvaccinated individual has 20x the risk of dying from Covid-19 than someone with a booster.
I am no first amendment scholar, but spreading lies that increase people rate of mortality by 20x seems pretty close to the "shouting fire in a crowded theater" exception to protected speech. That puts aside the fact that Twitter is a private platform, thus first amendment laws do not apply.
[1] https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety/ad... [2] https://www.cdc.gov/nchs/covid19/mortality-overview.htm