Is there a source for this? I wasn't aware of that, and it sounds interesting.

26,000 years sounds more like the period for Earth's axial precession. https://en.wikipedia.org/wiki/Axial_precession .

What you describe doesn't make sense. The Earth's orbit is effectively constant at that timescale, as are the asteroids in the main asteroid belt - otherwise interactions with Earth's would have changed the orbit.

There are conjectures of regular extinction events on 30-60M year intervals, but the data for that isn't strong. https://en.wikipedia.org/wiki/Extinction_event#Patterns_in_f...

Our star system has only a single asteroid belt, so if you are referring to it then the proper phrasing would be "the asteroid belt" (like "the moon" and "the sun"). And no, we (assuming that "we" is the Earth) do not pass through it at all.

If you are suggesting that we are passing through another asteroid belt, like the ones around Vega or Fomalhaut, then the damage done by passing so close to their star would far outpace the damage done by their asteroid belt!