It might not be solid wood...it could be veneer. If there are seams at the corners it's veneer wood --which explains the difficulty sanding. Real thin wood like this can only be sanded lightly.

If you fill the seams with wood filler and sand everything to a smooth finish, you can use a solid wood stain that will cover over the different shades of wood and filler.

Thank you. I think you’re right, it’s veneer.
I didn’t think a stain would cover over the different shades!

You may want to spray paint the gold trim black..

I would remove the decorative wood appliques

They were removed - shown in the 2nd photo.

I'm not sure the lighter areas would absorb the stain the same as the already stained areas...?

Maybe test a small area to see.