So, flu crossed the host-species barrier >100 years ago.
Following a cross species transmission event, we expect a high rate of evolution for some time as the virus becomes more "optimised".. ie, selection for variants that have better binding affinity, or increased transmission.... once "optimised", selection is slower as there are fewer opportunities for significant fitness advantages
so... for COVID... we would, in a few years, expect selection opportunities to be more limited (ie vaccine escape mutants)... the same as we have for flu now.
An intersting example for flu is H7N9.... in early 2013 we saw rapid evolution of this virus as it became more optimised to infecting humans... and then limited change for the following 7 years. Thankfully this one has "disappeared" due to mass vaccination of poultry.
I think that this is the paper that describes the original selection process :
https://www.eurosurveillance.org/content/10.2807/1560-7917.ES2014.19.25.20836?crawler=true
Oh, also! I forgot. The evolutionary distance of "delta" to "omicron" is about what we see in H3 influenza every ~2 years... hence a vaccine update. Its just that most people don't care that this year it was 3c2a flu vs A1b. You can see all the "variants" of H3N2 influenza here :
https://nextstrain.org/flu/seasonal/h3n2/ha/2y This explains why sometimes we have a really BAD flu year (ie 2017) - new variant, one that was not in the vaccine