The cake looks done but it’s not in the middle. Should I just keep baking it?
At that stage, there is nothing you can do but just bake until the cake is through. Baking by time is not advisable anyway, no matter if you followed the recipe exactly or not.
If you made your dough wetter than intended, the texture of the baked cake can be somewhat different than expected, it is impossible ot say how much different without knowing the type of cake and the amount of extra water (but even then, it would be a very rough guess). But you have nothing to lose by just baking it and using it. If it is a simple poundcake or the like and it turns out too dry because of the extra water, consider a light syrup soak, or glazing it with something nonpermeable (chocolate-fat coatings are good here).