Wouldn't it be wondrful if it was that simple ? You are playing a fool's game geathering wags accross the web in hopes of integrating them into a professional looking diy project. What you are trying to do requires trial and error tests using various woods and stains. To do so successfully requires the ability to READ each trial then use it for next trial. That ability is acquired through study and experience. Solicit help of a professional or ask local woodworking supply store for referral to an experienced hobbyist.

It's similar to a novice asking how to do a beautiful ballet. There's a host of people that can explain but the novice probably can't prefect it without being shown and months of work.

You have Bruce prefinished red oak in gunstock. These were common and trending in the early 2000's. You maybe able to still find it.

Do you have a closet you could remove some from, that would be enough to do the repairs you need to do. That way, you know it will match.

I have nearly the same floor. I was able to match it well enough to redo my kitchen, which came tiled but I wanted a seamless look in our open concept house. If there are any leftover pieces, take it to a flooring place. Alternatively, get samples from flooring stores and find a close match.
I changed the direction of the installation, too.

Home Depot has the floors, but after 20 years I doubt the new Gunstock color will match the old...fading. But, who knows?

A true professional floor refinisher can probably do the job.

https://www.homedepot.com/pep/Bruce-American-Home-Gunstock-Oak-3-4-in-T-x-2-1-4-in-W-Smooth-Solid-Hardwood-Flooring-20-sq-ft-ctn-CB924/100118026?g_store=&source=shoppingads&locale=en-US&fp=ggl&pla&mtc=SHOPPING-CM-CML-GGL-D23F-023_010_WOOD_FLOOR-NA-NA-NA-PMAX-7066701-NA-NA-NA-NBR-NA-NA-NEW-NA&cm_mmc=SHOPPING-CM-CML-GGL-D23F-023_010_WOOD_FLOOR-NA-NA-NA-PMAX-7066701-NA-NA-NA-NBR-NA-NA-NEW-NA-22891204500--&gclsrc=aw.ds&gad_source=1&gad_campaignid=22891204701&gbraid=0AAAAADq61UdrTt4v5KQIMWPOH_xIkH4xt