Cards such as Crimson Kobolds and Intervention Pact are showing up in searches as "colorless". Shouldn't they have the color identity based on the card frame?

This is an understandable question, but I think they're fine as-is? I thought a card's color was determined by its mana cost. If it has no mana cost, doesn't that mean it has no color identity (colorless)?

Not for cards that have no casting cost. For those, the card itself has a "color indicator" (i.e., the frame).

https://mtg.fandom.com/wiki/Color_identity

I've reported on this issue in the past.

It's a complication when inputting sorted cards because it's instinct to put Ancestral Vision with other blue cards, as it's numbered as a blue card. When I ran into the problem, I was inputting blue rares, so I'd sorted the database by blue rares, only to find what you found.