What's the best glue for a wood/metal sticking task?

[ThunderGarlic]

I'm having the stairs recarpeted in my flat. The plan is to paint them white and then have a colourful runner of around 2/3 width.

With the old carpet now removed I can see that while most of the stairs are in good condition, there are some gaps (4-12mm) at the edges in places between the wood and metal frame on which the stairs are built (I'm in a converted building so some interesting structures). Some gaps look too wide to just add a filler so I thought about laying down some wood quadrant or scotia at the edges and glueing this in place before painting.

Does anyone know what the best glue might be for this sort of job? It would need to be strong, suitable for fixing wood to metal, and flexible enough to bend with the motion of footfall on the stairs. Browsing B&Q or Wickes online, there are so many options!

Or is there some better way to deal with this? Stairs are new to me.

Thanks!

gorilla glue might do, but if the substrate is flexing, it will probably come loose.

epoxy resin is strong but sets vary hard.

post some photos please, they might spark ideas.

Thanks PigletJohn!

Some pictures attached.

It has also just occurred to me that I could glue just one face of the quadrant to the metal frame at the side and then add a small amount of a more flexible filler at the edge where it meets the wood.

I think I might pin quadrant to the steps, lightly touching the wall, so that if the steps flexed up and down it would slide against the wall and continue to hide the gap.

I think you want to avoid the risk of anything being able to fall into the gap and get trapped.