Here is a pretty good summary of the history of vaccine development.
https://www.medscape.com/viewarticle/812621_1
While nearly all influenza vaccines generate similar antibodies, Covid and influenza vaccines generate significantly different antibodies
Influenza vaccines generate antibodies against influenza Hemagglutinin proteins targeting sialic acid receptors
Covid vaccines generate antibodies for (S) glycoproteins targeting ACE-2 receptors.
In short, we have 80+ years of experience generating antibodies for hemagglutinin, and much less for (S) glycoproteins.
https://en.wikipedia.org/wiki/Coronavirus_spike_protein
https://en.wikipedia.org/wiki/Hemagglutinin_(influenza)