The first vaccines in 1933 were against A type influenzas, followed by vaccines against against B type influenzas in 1942.

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)