Debt isn't a component of inflation calculation but they are related. During Covid the US government increased the deficit (not debt, the derivative of debt) by a trillion dollars (no partisan stuff here, Trump did it first and then Biden). The infusion of money into the economy was one of the drivers of inflation between 2021 and 2025. You may ask, where did the money come from? I don't know. The government "borrowed" it, but from whom I don't know. Money "invested" does not necessarily get into the economy, but money invested in treasury bond gets spend by the government and definitely ends up in the economy.
I would love to have time (get paid?) to sit around and develop useful economic models. All I ever see is people offering simple cause and effect relationships (like I did above) without showing anything close to what I would consider a reasonable model of the economy.