what kind of damage will water in your transmission couse

Mostly corrosion if left in there , you can drop the pan but you never get all the fluid that's in the converter , but then I hear a total purge may not be good for it either even as a maintenance thing . I'd drop the pan and see what comes out . I've removed the coolant lines to the radiator , put one in fresh fluid and the out put in a waste pan with no ill effects that I remember . The hoses attached to the line should be secured .

Worse case, bye bye transmission. I would drop the transmission pan and see what comes out, of course this being a Silverado that’s easier said than done, but you need to do it, or have it towed to a good transmission shop and have them do the dirty work and check it over.

Water in an automatic transmission can be damaging, depending on how much is there. A little water is corrosive, but won't cause a great problem operationally. A lot of water can be detrimental as it displaces trans fluid and affects lubrication and operation of bands, clutches, and seals..... It doesn't sound like you have any experience with this and if you mess with it, you could destroy the transmission. A trans shop can evaluate the trans condition and do a proper fluid change, including all the flued; not just the trans.