Why not use the same hardwood?

Agree

Same wood. Put a mat at the door outside/wipe feet. Put a pretty, small area rug inside door if needed.

NO TILE.

Use the darker wood. That too.Much prettier,

I agree same wood as stairs and a good mat outside to catch the mess and another inside that is made for wood floors

" Carpet is being replaced with the light brown hardwood flooring "

You are not adding hardwood to stairs and having thehm stiill be to code or a safe stair. Every tread needs to be a certain depth and the rise of each needs to be consistent. You have neither if you "add" hardwood.