If large, rug size should be big enough for front feet of all seating to be resting on it, which doesn’t look possible with layout. Other option is to place a smaller rug in front of couch and to make it feel less awkward, add a coffee table. Suggest taping out different sizes to experiment. Rug colors in other rooms don’t have to be the same but your room‘s shades need to be pulled together, so I’d use a rug similar to one in picture and then add complimentary cushions.

Modernizing your living room (after taking down a lot of the small decor items, which date the room): --A highly patterned more graphic rug (doesn't have to be this one because I don't know if the texture is dog friendly, but this palette that goes well with wood floors, tan pieces, wood items: --Bolder art and no small pieces over fireplace: --More modern lamp on corner table--wood base echoes your other wood pieces but has more modern lines --Take down clock --Add modern basket of chunky wood logs on the hearth and remove all the small decor items there except for seasonal like pumpkins

Only similar ones https://rugs.com/dark-blue-6x9-darya-oriental-rug-5387728 https://www.homedepot.com/p/nuLOOM-Arlena-Distressed-Persian-Medallion-Black-5-ft-x-8-ft-Area-Rug-BDSM12B-508/302758871?

I think it’s a Safavieh Studio Leather rug: https://safavieh.com/rugs/studio-leather/stl816a Big A has it (others might, too) in lots of sizes: