Help me fix a gap in my mudroom cabinetry

Some context- this was one of my first woodworking projects I ever did… a lesson learned was just how much walls vary in measurement depth. Made this built in bench and locker a few years ago as one of my early woodworking projects over time this gap has expanded between the locker and bench.

While I’m not looking for absolute perfection, this remains an eyesore. The gap is about an eight to a quarter of an inch (wider at the bottom). It’s kind of too narrow to scribe a 1x and fit in, and also too wide for caulking. How can I go about “fixing” this?

Home Depot guy suggested backer rod and caulk. I’m never going to be able to get this perfectly flush but would like some options for my amateurish skillset.