What makes your room look cluttered is the ginormous sectional. The speakers and what not around the TV also don't help. You need a very large rug which has color and pattern. Everything is blue and gray so what you need is actually a rug with warm colors with just a touch of cool colors to save this room from itself. Also lots of art on the wall, most of it very large, to take away from the institutional look of what you have so far. I'd also recommend a glass and metal coffee table in order to have something that isn't dark and dense in this room. Drapes for the window would also help, and a floor lamp on the far end and a table and lamp at the near end if you have the room so you can turn off those harsh overhead lights.

You have a lovely room, very neutral. I love the idea of a cowhide in the sitting area and something textural, like flokati in the sectional area. Agree to stay away from grey, but any other neutral color would look great. I also like many of your choices, but would probably stay on the lighter side vs dark. Where are windows in the room?

Go to a good broadloom store. Not a big box, a dedicated carpet store Select a nylon, or a wool and nylon that works in your space, and have it bound to 11 x 14, or larger if need be. It isn't just about "brand". It is about choice of materials. Antrim, Fabrica, Masland all have lovely broadloom in nylon. You won't find any of them in Home Depot. No matter a selection ? Frequent vacuuming , avoiding BARE feet, taking care of spots and spills asap will help. Pottery Barn wools are tufted, not woven. They will NEVER stop shedding. Luxury wool will shed, but will stop in a bit of time.. Your vacuum matters. NONE of the luxury wool will stand up to Dyson which literally tears up a rug. Many luxury will say "suction only" .....despite they are luxurious.

This is the rug I ended up ordering!...I liked the colours of ffpalms but wasn't sure about the pattern and then I came across this...Its cozy and the colours are muted but match the colours of the stained glass...Thank you all for your help...I also love the piece of art on the wall but haven't purchased it yet. I will wait for the rug and then decide what I want there but thank you again @ffpalms for the idea to stack the windows and hang a piece of art...The wall looks busier but also fuller in a good way :) Thank you so much for your kind words! I'm really happy with the basement now...Our kids love playing down there and its the hangout spot when family comes over @plantsarefriends