While watching your TV, while sitting on a chair or couch, your eyes should be 1/3 the way up the TV screen. Clients of ours that refused this advice, and raised the TV higher up complain of neck aches.

plus the tv detracts from the fireplace.

LOL by now you know if TV watching as is is comfortable FOR YOU and that is all that matters. It does detract from the fireplace, however.

Ok, in my opinion, I would not put the tv on the the wall to the left due to the window reflecting onto it, unless you want to use blackout window coverings which you would have to keep them closed most of the time:/ Instead, I would replace and lower that mantle with an appropriate sized beam for an updated look and then you would also be able to to lower your tv a bit, then add some floating shelves on either side of the fireplace that would also tie into the beam mantle. I would need to see more pictures of the whole room to help with more ideas.
Hope this was helpful even though I’m a couple years late on this post, 🤪