I vote for a deep built in, bench on bottom, hooks for jackets, storage on top - no need to have an L shape. Looks like you are off to a great start!

Where does the wall on the left go? What’s behind the camera?

Please provide a floor plan, and define "etc".

This probably isn't the advice you want, but I vote that you build a closet to hide the coats, etc. Custom cabinetry will be very expensive unless you're doing it all yourself. Regardless, my mind can't handle seeing all my kids' coats, school bags, archery bags, etc. hanging out on full (and messy) display 100% of the time. Mine would never look like any Houzz mudroom ;)

If you do end up with a corner, I would make it a deep bucket space (with removable liner such as a metal bin for cleanability) that could be used for umbrellas, walking sticks, and other linear items.

Go to Pinterest and search L-shaped mudroom lockers, many ideas will pop up.

My confusion is where exactly is the 'L'? Is it what you're showing? Are you saying you have the 'L' and you just need help with that corner you're showing....if so, show the 'L'.