Nature.com doesn't agree with you. At least in 2019 it wasn't controversial to say so:
"Because mRNA falls into the broad vaccine category of genetic immunogens, many of the guiding principles that have been defined for DNA vaccines (162) and gene therapy vectors (163,164) can likely be applied to mRNA with some adaptations to reflect the unique features of mRNA." [0]
And still in 2021, Nature.com felt they were gene therapies:
"However, these mRNA vaccines, which have been developed and approved within a few months, signify a breakthrough in the field of gene therapy, which has battled to achieve ordinary acknowledgement due to a large number of sceptical and conservative scientists and other claimed safety and translational concerns."[1]
And the FDA disagrees with that definition of gene therapy:
"Gene therapy is a technique that modifies a person’s genes to treat or cure disease. Gene therapies can work by several mechanisms:
Replacing a disease-causing gene with a healthy copy of the gene
Inactivating a disease-causing gene that is not functioning properly
Introducing a new or modified gene into the body to help treat a disease" [1]
Yes there are competing definitions. However the important part of the grandparent remains unchanged. mRNA are extremely unlikely to modify genetic information of your body.
"Because mRNA falls into the broad vaccine category of genetic immunogens, many of the guiding principles that have been defined for DNA vaccines (162) and gene therapy vectors (163,164) can likely be applied to mRNA with some adaptations to reflect the unique features of mRNA." [0]
And still in 2021, Nature.com felt they were gene therapies:
"However, these mRNA vaccines, which have been developed and approved within a few months, signify a breakthrough in the field of gene therapy, which has battled to achieve ordinary acknowledgement due to a large number of sceptical and conservative scientists and other claimed safety and translational concerns."[1]
[0] https://www.nature.com/articles/nrd.2017.243 [1] https://www.nature.com/articles/s41435-021-00136-6