The water FROM the mushrooms is a product used in making mushroom ketchup. Not that it's common nowadays (or even the last 200 years...), but it is made, commercially and at home.
A point for judging the answer you should expect is that commercially produced and sold mushrooms can be reasonably counted upon to have been grown and handled professionally enough that anything inside them (as opposed to surface contamination) should be safe unless it is a well-known situation.
(And these are mushrooms: after all is said and done, while SOME mushrooms may be grown in manure, none of the industry is the cesspit that the chicken industry is and not too many worry about what they eat from their offerings, flesh-wise or internal liquids-wise.)
Not to mention but anything the liquid brings out with it SURELY had some left behind so if there were anything of concern, some would still be there when you ate the mushrooms and so the concern would be somewhat moot.
Of course, if you are still concerned, just dispose of it. Or stick an instant read into it and make sure it rises to a safe-seeming temp before you allow it to follow the food.
As to washing, mushrooms do NOT absorb any water from washing. While rubbing them clean (if done intelligently which... well, most people are pretty careless) ought to be perfectly fine and many are happy with them rubbed clean, I wash them any time I am not frying them. If frying in some manner, one doesn't need to increase water in the pan, even if it is surface water that was not fully dried off. Washing is easier and more complete (who wants ANY peat?) but drying is tougher. So judge your skills and act accordingly.
Mushrooms grow their cells but leave them "flat" or "uninflated" waiting for the right moment (and plenty of moisture) to suddenly fill them all with water and grow incredibly quickly. And reasonably quickly. Just depends upon the mushroom. Point is that the growers wait until they are just about done doing that so they are as big and heavy as possible before picking and shipping. So they are pretty much done taking in water by the time they hit the store. And surface absorption isn't their biggest source anyway. So not only do tests show you won't add water in prep, but the way they are grown and shipped ensures it won't happen either.
Naturally, if you have a special kind, or they were marketed at some special slice of the market ("baby mushrooms"?), there may be special circumstances about them.
And ALL bets are off if you (or anyone else) "picked them" (as opposed to grew them and sold them). Good luck with those.