Really? Do you have a reference for that? It doesn't match the experience of myself and others that I know. Everyone I know was talking about how great it was that they hadn't had a cold for so long, during the lockdowns.
Flu cases are tracked due to its severity. Cold cases are likely not often even paid attention to by many of those experiencing them.
Anecdotally, I and my friends and relatives hunkered down for COVID in 2020, and we had more cases turn out to be actually COVID-19 than common colds.
From this I made an uneducated extrapolation that the common cold pretty much stuck around somewhere and began to rapidly spread again as soon as people got out and about (I got one first week of schools going back in September, as per usual), whereas flu clearly did not.