If the door from the bathroom out to the hallway aligned with the window, you could leave the door open and that would let some of your natural light into the hallway. Of course, you would lose it for those time periods when the bathroom was in use.

It is possible that it might not look great. They seem most appropriate in homes with high ceilings and your ceilings don't look very high. But, try mocking things up first.

Take down all of your artwork. And use masking tape to layout on the wall common transom window sizes.

It would help if you installed a transom with trim the correct scale and style for your hallway instead of a contemporary trim-less transom.

You can use frosted glass. It will allow light through, but not show anything you don't want to show.

We had solar tubes in our last house, they were wonderful. One in the interior hall bath, one on the large landing, one above the stairwall. The bath solartube had an integrated fan, the other two had integrated lights. Never had to turn the lights on until 9 in summer, or even 5 in late December, instead of hall lights on all the time. No leaks.

Can you install a solar tube that would be the perfect answer but where are you? IN Britain there are so many rules about old building preservation .The transom makes sense but honestly what do you have there for the rest of the time lighting . I like hallways lit with good lighting all the time

Love my solar tube. When renovating our kitchen we had to remove a window that looked onto our sunroom and we put in a solar tube instead. Wonderful light and I do not miss the window at all.

Transom! In my daughter's renovation we used transoms in two bedrooms (operational for air flow) as they gave a solid wall for the headboards. Another operational one was used in the bathroom so we could close up a double hung window that was in the shower. For you an interior transom would brighten the hall and you still have an almost full wall left.

My builder recommended a solatube for an interior stairway that terminated into an interior hallway on the 2nd floor. The amount of daylight that provides is astonishing. Highly recommend! Wish I had put more in other places....