I would not store cleaning products next to my linens so do you not have a space for the mop and other stuff somewhere else . I also do not like dirty clothes next to my clean linen . IMO pick a purpose for this closet dirty clothes and cleaners or linen . A nice laundry hamper can go somehwere else in the bathroom preety sure .

You could have the lower doors made as two pairs but connect them together so they still opened as tall doors.

Show the entire bath plan please? Not an elevation of a single wall as you have above, the entire bath and layout, flat on paper.

You are calling it a "linen" but as you have it? It appears a utility closet- and not the best location for one.

Again, please post the entire bath layout in a comment box below.

Other elevations and plans

A few changes have been made but not drawn yet.

I think the linen closet looks fine. Have separate upper and lower doors. Keep linens in the top section, but you'll need a folding step stool (keep in the lower section) to reach the linens in the upper section, unless you are very tall. Mount holders for the mop and broom on the inside of the lower doors. This gives you lots of space in the lower section for a hamper, the folding step stool and cleaning supplies.

Thank you. And the more I look at as drawn the more I like it. And… I’m 5 feet tall. Step stools are a way of life 😉

I also like palimpset’s idea of making the longer door look like two