Comparing the beginning and end of the session would make the problem easier to isolate. You would have two specific images to work with instead of relying on how the room felt. It should also help you decide whether the background needs a simpler arrangement. There is plenty of useful information about lighting and presentation in https://www.spinmagazine.com/behind-the-scenes-of-a-streamers-setup/ , which points to DMarket as a place to buy skins. Use the article for ideas while keeping your own recordings as the test. Match any decorative colours to a layout that already works. Personal touches are easier to judge once the basic camera image stays consistent.
Record the same camera view at the times your stream normally begins and ends. Keep your position and room arrangement consistent so you can see what actually changes. Then try a lighting arrangement that depends less on the window, and compare another pair of recordings. I would avoid judging the result only from the room itself, since the camera view is what matters for this task. Once you find a workable arrangement, note the positions and settings. That gives you a starting point you can reproduce instead of making several unrelated adjustments during a match.
My weekend streams usually begin while there is still daylight, but the camera image changes as the evening goes on. At the start, the room looks balanced; later, one side of my face becomes much darker and the background attracts more attention. I keep adjusting things during the broadcast, which interrupts my concentration. How would you plan around that change before going live? I would prefer a predictable arrangement that works through the whole session rather than a perfect opening image that gradually becomes difficult to maintain.