How to brighten the hall?

I would make a very long wall hanging(s) out of many kinds of fabric, sewn or stitched together, in an abstract composition.

Then I would use a tension curtain rod or a shower rod to hang it.

Make sure that it is something that is ok with your rental contract. Do they allow hanging pictures, painting it, etc. If nothing else, check with the landlord or rental company to see if it is ok to paint and will they approve of the changes. Bring your ideas with you and paint samples with the color/colors you want to use, they may be more inclined to say yes if they can see what you are going to do is advantageous to the unit that you are in.

Command hooks are awesome for hanging almost anything! The can hold dowels for curtains, posters, wall hangings/art. Removal contact paper makes for great wall paper in rentals.

I places a string of white lights along the steps all the way up or down depends on where your outlet is that way you can see the steps

You can put led tape under each step or under the railing.

I live in a rental and had a dark hallway. I asked permission to use command hooks and rope lighting. Permission given and I put hooks and white bright led rope lights up. Walmart has rope lights in 25ftor larger at a good price.

A photo gallery wall would look great. Even large empty decorative art frames painted in a fun color would add interest. Then just under your handrail it looks like there is a piece of wood you could add rope light or Color Changing Flexible Self-adhesive Light Strip Complete Kit with 44 Key IR Remote Controller 24V 3A Power Supply https://www.amazon.com/dp/B01DZRN0NS/ref=cm_sw_r_cp_api_i_ox-JCbNMMXJEP]led light strips - they are cool because you can change the color and are inexpensive.

I would add mirrors. It would look great if you were allowed to paint the walls white, but if you aren't... Add some mirrors (start picking them up at thrift stores). They will reflect light and work great to brighten up an area.