Hey, I'm not an expert, but here is my best guess: the leaves appear to have completely lost their green color before turning grey. This could be due to losing chlorophyll, due to magnesium deficiency. How soon before you move them outside?
Maybe artificial light is bad for the chloroplasts too.

Hi.

It looks like an over-watering/drainage problem. Let the soil dry out between waterings. Stick your finger in the soil and, if it's still damp, don't water. Only water if the soil is dry.

Tomato plants don't like continuous moisture and soggy roots. Plus, too much moisture can lead to other problems with seedlings, like damping off.