That's actually a worst case scenario. COVID-19 mutates a lot more slowly than influenza. The reason we're getting so many variants right now is we have so many cases, and each case is an opportunity for mutation.

Once we get COVID-19 down to endemic disease levels, the much slower mutation rate should mean boosters needed less often than annually. Checks on trial participants have shown only a small amount of waning immunity after six months.

We may need annual boosters through, say, 2025, because of slower vaccination rates in other parts of the world, but my guess after that is every few years or possibly if you're traveling.

Moderna is working on a combined shot and if the worst case does come to be, other companies will too, so with luck it will just be one shot for both.

There's also research into a pan-coronavirus vaccine, which would be easier than a pan-influenza one, would give at least some protection from the next novel coronavirus (coronaviruses like to jump species) and also reduce the number of colds you get by a certain percentage.

And if you have the time/energy you can look at the actual papers from the trials, but they are kinda written in Biologist, if you know what I mean.