Can you install a transom?

Transoms are almost always a good way to get more light into a room. Light wells or light tunnels that are installed in attic spaces or even wall chases will bring light from the roof to interior areas. Perhaps the easiest solution is to install more lighting fixtures in the hallway or at the very least switch out your existing light bulbs with higher intensity ones. Good luck!

The only way to steal light from another room, is by construction and leaving all the doors open.

There are other changes that can help though. Painting with a high gloss white paint will not only feel crisper and lighter but the finish will reflect more light. You may want to read up about its pros/cons.

https://thouswell.com/why-high-gloss-wall-paint-behr-paint/

Add a large mirror, a light coloured runner will break up the darker flooring, and more reflective pendant lighting and ideal bulbs. Would be even better if you could duplicate at other end of hall. Instead, pot lights could be a great addition.

Honestly get a much better light fixture one with at least 3 heads in LEDs 4000K and that space will look light filled Do not use high gloss white or any other color paint it will show every tiny little bump in the wall finish. a piece of art that looks like lookung out a window is also a good idea. BTW do not choose any fixture with an Edison bulb ever anywhere. There is a reason they fell out of favor they give horrible yellow light.

Thanks all for the comment, it is due to be repainted and new light fitting makes sense. I think I may look into the idea of glass above the door, not the cheapest but worth checking

Install a solar tube in the hallway. They are great!

Removing that wall entirely would give you the most light, but would require a repair to both the ceiling and the floor. Widening the doorway is simpler because you don't need to do a ceiling repair.

Either way you need to do a floor repair. Easiest if you have some of the original wood, which you may have in a closet. My son did a similar repair and used a flat threshold in the same colour wood across the whole opening. Looks fine and he loves the light that the area now receives.