That may well be so, but it is not at all clear that the Supreme Court itself understands the distinction. I say that because of a recent decision by that Court. That decision was Trump v. Anderson (2024) which dealt with disqualification under section 3 of the 14th Amendment.
In that decision...
I have read that US law (much like, reportedly, British law before it) makes a distinction between a federal office such as the presidency and a legislative seat such as ones in Congress. That is to say, legislative seats are NOT regarded as offices.
For example, that distinction can be seen in...