Dude, relax. You went on an eight paragraph(ish) assumption laden diatribe in response to a simple two sentence statement of fact.
For starters,
read up a little on how viruses evolve.
There are "big" changes and "small" changes, and
there are multiple ways those changes can occur. (Including, but not limited to,
reassortment, which i believe is what you mean by "assemble randomly".) They're all "mutations", because "mutation" just means change. (There is an implication when using the word that they are "natural" changes rather than due to genetic engineering, but i'm not sure if that's a connotation or denotation.)
The H#N# nomenclature just describes the proteins on the outside. It's possible for mutations to occur in the rest of the virus without changing those. For example,
there are multiple strains of H1N1. Because the outside as the same proteins it will mostly "look" the same to your body and prompt a similar immune reaction, but if you asked a trained immunologist they would probably say it's more complicated than that.
So A: no one claims the old viruses "go extinct" or "vanish", but B: even though the old strain is still around the H1N1 you catch this year may not be "the same damn virus" as the H1N1 you caught last year. (Or whichever major H#N# strain happens to be making the rounds, H1N1 is just an example.)
Also, technically, the evolution of a virus from one strain (minor or major) to another probably takes less than a second, at the moment the first virus with the new mutation is replicated. So yes, overnight. However how big a change it is and when it occurs is a matter of statistics, it could occur tomorrow, or ten years from now.
In fact given how many viruses of a given strain there are in existence at a given time and how often they replicate there probably are multiple mutations happening every day. However most of those mutations are either detrimental (the new virus either "dies" or fails to replicate) or inconsequential (the new virus fails to outbreed the parent strain and never gains significant numbers.)
Once the new strain exists how long long it takes to spread and become a dominant strain is partly a matter of statistical randomness and partly a matter of how effective it is at spreading compared to the parent strain. So the next strain of the virus that causes Covid might just have mutated while i was writing this post, but it might take weeks or months or more before it spreads enough to be identified and cataloged.
And whether any new strain is more or less deadly than the previous one is pretty much a crap shoot. Being less deadly _tends_ to be favored by natural selection in the long run, but in the short run being more deadly can be advantageous if that change also comes with improvement to infectiousness. In fact if viruses "knew" they should be less deadly and had any choice in the matter there wouldn't ever be pandemics in the first place.
"Why do we have new vaccines every year for 4 or 5 strand of flu? Oh: because flu did not know it should have "evolved" into "non deadly" a millenia ago"
The fact that you can get the flu multiple times over multiple years without dying in the process is pretty good proof that it has (in general) become more "non deadly" than it has been at other points in history. (Partly due to better medical treatments and humans developing antibodies, but partly also the virus adapting to us.)