No, you're not being silly. After the Mueller investigation concluded, Trump proclaimed that he was owed an additional term because of all the investigations, so that makes three terms that he felt he was entitled to serve. He never conceded the 2020 election and never recognized Biden as a legitimate president, so in his mind I'm sure that he feels he is "owed" that term, making him (in his mind) entitled to four terms.

You have to remember, the rules have never applied to Trump. His entire life he has bent and broken rules, laws, and customs. He has no respect for the Constitution. It doesn't apply to him, only other people so it is not surprising that he didn't bring up the 22nd Amendment. It is irrelevant in his world.