Congress can only remove the disqualification, they can't impose it.
It's a problem that the amendment doesn't tell us how it's supposed to work, but the fact that other disqualifying factors (age, residency, etc.) are determined by the states suggests that the states can determine disqualification on the insurrection factor too, and through the same procedural mechanisms.
Congress should pass a resolution removing Trump's disqualification.
That would satisfy the 14th amendment without setting a nasty political precedent while at the same time serving as an official recognition that Trump committed acts that triggered the 14th amendment.