They definitely care about second-order effects. If for example they raise the rates enough that debt servicing starts to become a real issue and this leads to higher taxes and spending cuts, then that is an extra economic headwind which they must consider.
They don’t care about the debt figure per se but they do care about the economic implications of that debt, and how other entities are likely to react to it.
> If for example they raise the rates enough that debt servicing starts to become a real issue
then they would've realized they hiked too much. That's why the current Fed hikes are conservative - a lot of people are claiming that they are late, and should've done it earlier, but i think they are doing it right. Slow and steady, and be conservative.
They don’t care about the debt figure per se but they do care about the economic implications of that debt, and how other entities are likely to react to it.