My first quick thoughts are a nicer more substantial banisters (on both sides of the staircase), and an upgraded carpet runner. Treat the staircase the same way you would one that leads from your front entry to upstairs bedrooms. It's not shown in the picture, but you do need good lighting on any staircase. Is there a ceiling fixture at the top? If not, can you put one there?

A cottage on a pond!! You could rip the runner off, and have fun painting the stairs like a large canvas to suit your whimsy with bright colors. Add a bright, larger banister, and paint ceiling and add lighting.

Yes, brighten the stairs with color and whimsy. Sconce or other lighting would help immensely.

Search for painted stairs, and you will see Many different styles.