I lifted my area rug to clean my living room when I bought my new couch and loveseat. As soon as I lifted the rug, I realized that the floor underneath the rug is much darker. If I keep the rug off the floor, will it eventually catch up with rest of the floor? I'm certain this is due to wood aging and fading from the UV light. The area affected near the floor is near my patio door and i keep my vertical blinds open typically.

Has anyone tried to keep the rug off the floor method and if yes, how long did it take for the wood to blend in?

I have extra spare boxes of my floor and can quickly get this changed as its a floating engineering floor but my worry is this is going to happen again? Is it worth to go thru the trouble and get this fixed?
What if i keep my.blind shut if i get this fixed? Will this fading happen regardless?

Wood flooring is susceptible to bleaching or fading from light. Once you have a photograph of the rug on the floor it will probably never blend in completely. If you want to try, you would cover the faded area with something like newsprint paper and then open the window during the season when the light comes into the room directly so it is bright with the rug moved away. Sometimes this spot will not go away even with sanding the floor to try and remove the faded area. Light does penetrate into the fibers at the surface to fade the wood below the surface, too.
If you replace some of the flooring with new, this will be brighter than any fof surrounding flooring.
If you would like for your flooring to age more gracefully taking the rug outdoing part of the year will allow it to fade evenly. Staining the floor dark will help protect it from the UV rays.