The reason they did so was they were just using a rule of thumb that applies to all flights and they want to be able to encourage airlines to adopt the known practices that can avoid these extra emissions (shifting time of flights is the big one I think).
There's no standard yet for estimating them though, but they are working on one:
https://airqualitynews.com/2022/09/01/is-google-airbrushing-...
Water changes it behavior depending on the relative amount in the air. A sufficiently high amount will act on visible light (contrails, clouds, fog, ...), but even in its "transparent" form it messes with wave lengths outside of the visible range.
Contrails are created by local changes of temperature at the wing tips (turning the invisible water into visible, temporarily) and by adding water as part of the exhaust. Burning CxHy leaves some H2O, visible or not.
I would have guessed that the visible form is contributing more to cooling than the (probably more common) invisble form. Possibly a matter of when they turn invisible, which might be more likely in the morning than at night (those produced during one day staying visible during the night helping with heating but vanishing next day, not helping with cooling).
Modelling water properly is quite surely complicated, with bigger effects than CO2. Not only for contrails.