> So out of thousands of protesters, three were armed
Many were armed only four (one based on substantial investigation after his initial arrest and subsequent initial indictment) have been charged with firearms offenses; most of those in solved were not arrested and searched on site, but later based on video evidence, witness testimony, and other evidence. (Assuming I’m not missing more, the summary page presentation is not consistent in how offenses are described, and I haven't dug in and reviewed each of the detailed supporting document for each defendant.)
> How does occupying the Capitol building translate into controlling the government?
The specific plan was to use threats and violence to, in order of preference:
One, convince the Vice President to as Trump had publicly advocated and Pence had publicly indicated he would not, refuse to open certain electoral votes, ask Trump-friendly state legislatures to “recertify” them, so that those legislatures would replace the publicly elected slate of Biden electors from their states with legislatively elected Trump electors, or:
Two, render the Vice President, if he remained obstinate in his refusals of participation in the auto-coup that Trump had publicly called for, and any similarly uncooperative successors, incapable of presiding (the chant “Hang Mike Pence”, and the gallows constructed for that purpose, indicating the method of incapacitation planned) so that an official on board with the plan would take over the gavel and act as described.
The successful evacuation of members prevented the plan from working, but that was the not-very-secret plan.