These are some of the Gavin considering.

" I’m thinking I need to pick a rug first, then order the chairs with a coordinating fabric "

The first thing to pick is the one that will last the longest.

The cool tone blue and grey clash with the warm tone beige walls - paint the walls. Note that grey is a color that is going out and was never a pretty color to begin with - not sure it is a good idea to spend more money matching something trendy that many think is ugly. Be sure the rug is machine washable - a cotton rug from IKEA could work.

This rug is a bit lighter than you need IMO.

Some kind of would work better

https://www.rugstudio.com/surya-cappadocia-cpp-5027-area-rug.aspx

Your house is really pretty. Maybe something like this from pottery barn would work. It seems like it would pull the warm tones from the wall and the grey from the couches.

Belrose Hand-Knotted Wool Rug | Pottery Barn

https://in.pinterest.com/pin/746964288288224073/

Beautiful room. I love the warm walls and wood beams. I agree with the suggestion of the Pottery Barn rug as it pulls the greys and browns together. You walls are warm and the rug you posted is too cool.

I don't see how you have room for any more furniture in here. How could any walk past two swivel chairs in here? Take two chairs from other rooms in your home and place them where you intend the swivel chairs to go and then post a picture of them.

How many people do you need to seat in here on a regular basis? Before investing in swivel chairs, I'd instead purchase a second full length sofa to replace the love seat. It is a better way to get more seating in here.

I have two full sized sofas in my living room in an L shape and love it. We can really seat a crowd.

Thank you SO much! Your opinions are so helpful! The visualization helps so much! I love the rug suggestions, though my budget is a bit limited after a big renovation.
Great point on possible chairs /furniture too. We frequently have 8-10 adults here for gatherings. I have a more narrow swivel picked out , but was a little concerned having enough space. I will check to see if a matching grey couch is still available.
Thanks again!

I loved this rug and ordered it for this room

Oops. Sorry. Wrong rug. I ordered this rug.

This is the LR next to the FR. Any ideas for a coordinating rug in the LR? All advise is greatly appreciated!

Would this coordinate ok with the FR rug? Is it too busy? I’m having a hard time finding the right rugs!!

Or this rug?

It looks darker in photo.

Calvin Klein Ck950 Rush Modern Indoor Rug, 8'X10' - Contemporary - Area Rugs - by Nourison | Houzz

Your renovation sounds fantastic! It sounds like you're creating a beautifully cohesive space with those color choices. If you're looking to add a unique and artistic touch, have you considered incorporating a mosaic into your design?

A custom mosaic on the wall behind your couch or above your fireplace mantel could add a stunning focal point that ties the entire room together. Our mosaics can be customized to match your color palette, complementing your grey couch, blue ottoman, and the new rug and chairs you’re planning to add.

We'd love to help you explore some design options that could enhance your space even further. Let us know if you're interested!