Is engineered timber, mdf, bamboo or full timber?

Engineered timber

If you know the manufacturer’s name I’d check their site first specific advice. There are also repair videos on YouTube. It may be worth considering some type of protection product for the edges.

Hi HU, this looks like solid timber (European Oak) to me. To repair these I would carefully remove the splinters taking care not to pull into the undamaged timber and then give these corners (only the corners not the faces) a light sand with a fine sandpaper along the full length creating a small Aris edge down to the depth of the missing splinter. Then seal the exposed timber aris.

These Arises should have really been done when the staircase was first built.

Hope this helps, Malcolm.

Looks like a mitred edge which is unforgiving