Like your bench. It looks great.
For the drawer, if it fits in nicely and if this is just for the garage or not a museum then perhaps these ideas:
- as the drawer slides in and out, but hasn't support, why not add runners to the bottom of the cabinet itself and two or three timber pieces to the underside of the table top. The back top edge of the draw would rub against table underside runners preventing it from tilting, and the runners on the bottom support the draw with gravity.
- a dowel or biscuit on the top edge of the back draw would stop it from sliding all the way out. Fit it so it sits between the table underside runners. Tilt the draw front-up to get it in.
- as mentioned by another, but a small elaboration, use a screw in the rear left and right walls behind the draws to allow for adjustment. Rather than one on the centre, as the draw doesn't have sliders it won't go in straight, but the two screws, when adjusted appropriately, will force the draw to sit at both the right depth, but will be flush with the front (if angled, screw one or the other in/out a smidge
BTW, I don't think it's rookie to have enthusiasm. The way you have done it is normal. So many drawers from cheap furniture places (here's looking at you Hardly Normal) and also every old dining room cupboard and bedroom chest from the past used this method. (I don't think ball bearing dual full length metal retractable runners were too common in the 18th century . )