Gaia Gbp - Grp: why does it get larger as star gets redder?
But you demonstrate that you know the answer to this question! Fainter objects have larger magnitudes. So as the white dwarf becomes cooler and redder, its blue magnitude $(G_{BP})$ grows by more than its red magnitude $(G_{RP})$ and the colour-index $(G_{BP} - G_{RP})$ becomes larger. This is very similar to the commonly used $B-V$ colour, which is larger for cooler stars.