I'm no biologist, but mRNA is ephemeral by design - it's constantly being broken down in the body. The fact that mRNA is converted to proteins by ribosomes is one of the best understood processes in cellular biology, and synthesizing the mRNA for a new protein is not a new idea. Getting actual viral vectors injected into my arm seems much more concerning on the surface (though it's obviously also very safe).
Were that it was so simple. My understanding is the mRNA used in the vaccines was engineered to be more stable (less ephemeral). Not sure what that means in terms of half life, but AFAICT it's a mistake to assume that it will behave similarly to naturally occurring mRNA if this is true.
They put a lipid coating around the mRNA to protect it. But as soon as that coating is removed, it will be quickly be broken down in the body by various enzymes.
I'm no expert on this but the lipid coating allows it to enter the cell where the coating is removed and the reverse transcription happens. I've read that any of the mRNA that is injected will be gone within 2-3 in the body.
If it can be reverse transcribed then so can Covid which has the same mRNA as the vaccine and way way more. Plus, covid infects a million times more cells than the mRNA vaccine.