Curious... what was the rational to not match new floors to existing tread and handrail stain?If you prefer lighter wood tone (your new floors) you'd need to remove spindles & railing and either sand & refinish (depending on wood species - are treads and new floor same type of wood?) or replace treads to match new flooring... From experience it's a big job! Where did you purchase the flooring - do they sell treads? If not, suggest you speak to a few flooring & stair specialists (not just big box store sales reps no offense meant). When we installed our h/w floors the flooring store's installers were able to sand & match our existing stairs to the new floor...but we had the same wood species (oak) on both...
Hope this helps.

What about a black stain, if you have to keep the treads and railing?

Thank you both! I think I really want to find someone that can help me change the treads and railing! I just need to figure out who can do the work.

Search out flooring stores - NOT Lumber Liquidator types though - on Houzz, Google, etc. They will have stair contractors they work with.

My daughter did a gut rehab and had wooden balusters and Newell post. Had to replace some of the flooring and restain It all. She had all of the stairway wood sanded in place and restained to match the new floor color. It was tedious and she had to pay of course. But the result was beautiful.

I cant find a pic of the stairway but it matches her floor perfectly. All red oak.

personally, I think with your light floors your stairway would look really good if it was several shades darker than the floor...minus the orange shade.