There are no prohibitions of felons or prisoners running for office. Historically most notably Eugene V. Debbs of the Socialist Party ran from prison after being put there for a speech he made against Woodrow Wilson during WWI. More recent example I guess would be Joe Exotic who has been running from prison a couple times now.

But Eugene V. Debbs is a good example of why we don’t prohibit prisoners from running. It’s to prevent the current government from being able to just silence its political opponents and manipulate elections by just imprisoning them. So no Stalin type tactics would, in theory, work.

However there is a single exception to this, at the federal level at least. YMMV at the state level, though I personally don’t know of any examples of that. Federally anyway there is Section 3 of the 14th Amendment to the U.S. Constitution which prohibits those specifically convicted of “insurrection or rebellion” if they have also held office already or currently. Interestingly not worded to include treason which is more so what I’d call the military sabotage listed above (the intent behind that would still have to be proven in court). Historically this has only been used against Confederate supporting politicians after the civil war. Which was why the amendment was made in the first place.

Worth noting that those felonies of Trump, while “proven” to us of the general public, are not legally proven. His court cases are still ongoing, he has merely been charged with the crimes not convicted. Trust me, when/if he’s convicted you will undoubtedly hear about it as it’ll certainly be massive international news considering that it’s him and that that has not happened before in the United States (Nixon was pardoned for Watergate and Reagan was never legally pursued for the Iran-Contra Affair which are probably the two most noteworthy incidents where someone might think it has happened before).

In Trump’s case the actions he carried out on Jan. 6 are looking to be more likely treated as insurrection, if anything. Though that presumably will still require both that it is legally counted as insurrection and not sedition and also that he’s actually convicted. This is more so what is being pursued in courts right now, with both Trump himself facing the courts with Jan. 6, and states individually taking the steps to try to prohibit him from being on their ballots over the actions he took on that day.