I'd sponge up the water and clean up the mold. Then, look for more water leaking. Since it's being replaced next week, I'd probably not do anything else at this time. FWIW, the new ones available today WOULD have a problem standing in water as their air intake is often literally at the floor. The older ones usually have feet, and the air intake is quite a bit higher. If the gas valve was submerged, it would be a different story...that can be dangerous, but I'd doubt that's an issue.
Note, if it's leaking from the T&P valve, that may not be a WH problem, but with a WH 13-years old, replacing it is a good first step. A leaking T&P valve may be a symptom of a failed expansion tank, or the lack of one, if you have a closed system. Water utility companies are often replacing their meters and installing a check valve, which makes the system closed. If you don't have an expansion tank, the WH can weep water each cycle as the cold incoming water gets heated since the pipes won't expand, but the water does - it has to go somewhere. The fact it's not rising could be that it's evaporating as fast as new stuff is being added - it had to come from somewhere! Could be a tank leak, but could be from the T&P valve as well, or even the drain valve.