Wood – Is it OK to use 1/4“ OSB over a standard subfloor before installing 3/4” hardwood on top

It's impossible to say for sure from your picture since it is already stained. But generally speaking the approach to this is trial and error with scrap pieces. You'll want to make sure the piece of totally dry before comparing the colour and it can look quite a bit different when wet.

It's unlikely you will get an exact match even using the exact same product since wear and tear and UV take their toll on floors. The only way to get an exact match across both floors is to refinish the old and new with the same product.

I'm not an expert, but here is what I found out when I redone my bathroom.

The OSB is used to add stability to the floor. When walking around, if you're only on plywood, the floor will bounce; simply adding the hardwood floor over the plywood sub-floor will not solve that issue.

When installing the OSB, using floor screws is sufficient. No nails, as these will move and you'll end up hearing them. And while you're at it, you should screw the plywood to the joists if it's not already done.

And if you could get tongue and groove OSB, you'd reduce even more the risk of hearing your floor ;)