Okay, so this isnβt actually about hydration, itβs about the fact that SSRIs commonly cause dry mouth as a side effect due to anticholinergic effects which reduce saliva release Some SSRIs are worse than others, and older TCAs are worse still. But OP is not dehydrated.
Water is great for hydration, but it is unfortunately not very effective at managing dry mouth due to these side effects. Flavoured beverages typically work better because they promote saliva release.
I would suggest OP add something with a sour note to their water, like lemon or lime juice which are unsweetened and have effectively no caloric component. Alternatively even just a splash of carbonated water will also work as the bubbles are irritants and will similarly stimulate saliva release.