There is no reason it would.
Barring some random unlikely mutation that could have happened anyways without COVID, there are no pressures selecting for greather lethality in the multiple influenza strains running around.
If anything, COVID will result in a less deadly than usual situation (I mean as we saw this year) because COVID is murking most of the likely targets. Basically COVID is picking off those who would have died from the Flu, plus some extra, competing* with the flu but also leaving less targets in the future. The only group at risk from the influenza that is safe from COVID is toddlers, but even then there's still no reason the flu would "come back with a vengeance".
No shit!
It's so frustrating having called this shit almost a year ago that the virus was here to stay and "defeating" it was a pipe dream born from unchecked human hubris; yet here we are being proven right but still losing because the twats in power still find a way to spin it to their own benefit.
Yes and no.
Prescribed antibiotics are the cause for resistant bacteria, and certain special proteins they put into handsoaps to a minor degree (though the later is somewhat disputed). Basically specialized enzymes and other compounds that inhibit some facet of the bacteria (or virus, but usually bacteria). For example Penicillin produces a "beta-ring" that lassos the bacteria's cell wall and stops their reproduction. It can be resisted with a protein that's basically scissors that cuts the ring and lets them reproduce.
On the other hand, shit like hydrogen peroxide, alcohol*, bleach, etc., etc., basically kill the bacteria and viruses by fucking evaporating and dissolving them.
Compare this to killing humans with ricin versus killing humans with napalm and lava.
Lastly its worth noting that the pathogens aren't "evolving" new features, as much as we are just killing 99.99% of the ones that don't have the resistant traits, and leaving the resistant ones there to reproduce.
*now some shit can develop alcohol resistance, but that's more so they can survive in decaying fruits and other biotic decay acids than the result of human disinfection