Sound diffusion panels--do they reduce brightness?

IME no. Looking at your room, your speakers and seating position are well away from room boundaries. I would look to a change in amp or cables.

Doors are closed behind sofa now. Amp and cables just upgraded

If your room is bright, changing amps and/or cables is not a solution. Although you have bass traps and an open space behind the listening position (all help), your room still has a huge amount of reflective hard surfaces, especially at ear level and above. Adding wide-band absorbers at the first reflection points is a great first step. If that step is subjectively effective, consider more.

Kal

IME, yes. I have used both the rear panels and those at the first reflection points. Speakers are well away from the room boundaries. I have also used the free standing Furutech panels. The latter can be moved around and give you some idea of what improvement can be made at different locations. I use one directly behind each speaker and in the center between the speakers. I use many different speakers and amps and have found the improvement using the panels not matter what the 'chain' is. Getting room treatment right takes time and effort. I've use EQ wizard software to do room analysis and that helped me 'see' what I was hearing.

Two other issues are the equipment and the recordings. You didn't mention the make and model of speakers or the other equipment involved. The reality is the current fashion for a lot of audiophile gear is to sound bright. That's not meant to imply everything out there is bright, but the odds are not unfavorable.

I imagine you intentionally chose the gear you have now so I presume it sounded correct to you at some prior point. You might want to compare that previous environment to the one you're in now.

Recordings are also often bright. Close miking and the generous use of EQ and other effects are very common. Even classical recordings are not immune to this issue. Does your brightness problem occur with all recordings or just some?

The tonal balance of my system is just where I like it on an overall basis, but my biggest frustration these days is the variability in recordings. It never ceases to amaze me how many releases are poor and artificial sounding.