mRNA has been studied since the 1980s. In 1990, researchers at the University of Wisconsin managed to make an mRNA vaccine which worked in mice. So the mRNA technology is not all that new. For example, google "Katalin Karikó".
What was lacking was funding to develop mRNA beyond academic research. DJT drove the necessary funding through operation warp speed.
The Pfizer/Biotech phase 3 trial involved 43,661 volunteers. The Moderna Phase 3 trial involved 25,654 volunteers. Since then 165 million people in the US have received the full dose of the vaccine (either Pfizer, or Moderna).
Historically, any long term effects from vaccines is known within about 8 weeks after the start of mass vaccinations. We are well past that point.
This is not really specifically due to the mRNA vaccine. According to 42 U.S. Code § 300aa–22,
enacted in 1986, "No vaccine manufacturer shall be liable in a civil action for damages arising from a vaccine-related injury or death associated with the administration of a vaccine after October 1, 1988, if the injury or death resulted from side effects that were unavoidable even though the vaccine was properly prepared and was accompanied by proper directions and warnings."
https://www.law.cornell.edu/uscode/text/42/300aa-22
Needless to say, 1986 is well before the covid vaccine so this is a bit of fear mongering.
Coronaviruses are known for undergoing rapid mutations. As such, the science will keep changing as new mutations develop.