You have a lot going on texture-wise so I'd probably keep it simple in terms of rug texture or there'll be too much going on at once. Warm would do well in this room though, so that's good! You mention it's away from the light outdoor area, is this photo an accurate representation of the lighting you normally get in this room? So in summary, you might want to have a look at rugs that don't have much texture, and are a bit brighter in colour to help brighten up the room. Below are just a couple of examples of rugs that could work, and one more neutral example.

Here are a few articles which may help: [https://www.houzz.com.au/magazine/11-area-rug-rules-and-how-to-break-them-stsetivw-vs~222609[(https://www.houzz.com.au/magazine/11-area-rug-rules-and-how-to-break-them-stsetivw-vs~222609) [https://www.houzz.com.au/magazine/how-to-choose-an-awesome-area-rug-no-matter-what-your-space-stsetivw-vs~9361652[(https://www.houzz.com.au/magazine/how-to-choose-an-awesome-area-rug-no-matter-what-your-space-stsetivw-vs~9361652) [https://www.houzz.com.au/magazine/finding-the-right-size-rug-for-any-room-in-the-house-stsetivw-vs~32205851[(https://www.houzz.com.au/magazine/finding-the-right-size-rug-for-any-room-in-the-house-stsetivw-vs~32205851)

Can you post a close up picture of the wood showing the grain, please?

given the luxury of generous available space i like outdoor rooms to be bigger than inside.. especially if they'll be used for entertaining more people than would normally fit into the same space inside and some outdoor furniture looks so cramped without lots of space to walk around