I think the concern is how the immunogenicity from a booster dose would pan out over time. It deteriorates over time and this study was done to confirm that there is still a sufficient level of immunogenicity 3 months out. I wish they have more data at different time points, perhaps within a 12 month time span.

I think it's a legitimate concern whether one should "time" the booster shot to coincide with peak flu season. I believe study on the primary doses conclude that full immunogenicity is reached in about 2 weeks? You're also correct that one should consult your doctor for advice more relevant in your local area.

Edit: here's a CDC report

> During the period of Omicron predominance, VE against COVID-19–associated hospitalizations was lower overall and waned with time since vaccination: VE after a second dose declined from 71% within 2 months of vaccination to 54% among those vaccinated ≥5 months earlier (p = 0.01). Among recipients of 3 doses, VE against COVID-19–associated hospitalizations declined from 91% among those vaccinated within the past 2 months to 78% among those vaccinated ≥4 months earlier (p<0.001).