Let's just capture the comments as an Answer.
Pull the drawers out and scrape or sand the surfaces (often referred to as "slides") that bear on the carcase (sometimes called "rails") down to bare wood.
Do the same for rails, as well. Both of these bearing surfaces should generally be free of any finish. There may be very hard and fast-drying finishes that wouldn't wear down and get sticky, but I suspect that would only be for special applications.
The idea here is to remove the finish on the bearing surfaces, or those surfaces that are intended to ride on each other in a relatively low-friction manner. You don't have to remove the finish on surfaces that do not touch each other.
Just rub a fine coating of wax on the fresh wooden bearing surfaces, reapply when you remember (like, every couple of years) and that's it.
As an aside, wax, especially beeswax, may seem sticky, but that is just a little static friction that is easily overcome. Then the wax conforms to the force and softens almost immediately so the slides and rails ride over a very low-friction surface. More to the point, it continues to do this over the lifetime of the furniture, unlike some finishes that may even cement together over time.
Of course, another option is to retrofit your design so the drawers take mechanical slides and rails (often in single installable packages) but that is beyond the scope of this answer.
