The virus is continuously mutating to be more infectious and/or resistant to immunity (some mutations are more advantageous for one than the other) so that it can keep reproducing. I don't know how quickly COVID does it compared to flu, but that one and the common cold will mutate every year and so we'll keep catching them till we die. For the flu we look to the southern hemisphere to see what strains are becoming dominant during their winters so we can prepare the next round of vaccines. It's kind of a very well educated guess.
With COVID we've got tracking all over the world to identify emerging strains more quickly and thus keep on top of preparing new vaccines. But it'll be pretty much a round the year task from hereon.
Just a couple of comments on your excellent post ...
1. Viruses will be mutating all the time, and some mutations will enhance its activity while others will reduce it. Those activities include the ability to bind to its target cells, which is in general an indicator of how fast the virus is taken up by the cell and starts replicating, the point at which it causes the disease. These (for Covid) are usually mutations in the Spike coat protein which we heard so much about when a new variant was doing the rounds. Other mutations may affect the actual ability to cause the disease itself. The hope was that a mutant would emerge which spread faster but had lost the ability to cause severe disease. This may have become fixed in the population and out-competed the more severe strains.
2. The overall mutation rate of Covid has been shown to be about 25 times LOWER than Influenza A virus due to a proof-reading mechanism in the proteins which replicate the viral genome.
And to reiterate, no mRNA molecule (vaccine or otherwise) can directly alter the genome of any cell it enters. Its purpose is to be translated to produce the Spike protein which then gets recognised by the cells (and other non-cellular components) of the immune system to generate an immune response. This is very long-lived, although does reduce over time, hence the need for booster vaccines.
