Ok, now onto the desk. I bought sheets of plywood and cut them into several different sizes. My plan was to experiment with various depths and then different widths to find the limits. I wondered how large the desk could be while still keeping the desk reflection under -20 dB. That was my goal. I also wanted the desk to be foldable so I could tuck it away, allowing me to move the sofa and table close to the TV when watching movies. Also to create more room for using my VR headset. I can slide the living room table next to the sofa, and then the desk, when folded, fits between the sofa and the table, leaving an empty space for that purpose.
There are a lot of pictures from this journey, both of the desk and the resulting ETC. I'll try to keep the pictures to a minimum to prevent this post from becoming a mammoth.
First try: 70 cm deep.

I placed the plywood on a keyboard stand.

The result: Desk reflection was -8.4 dB. Too loud!

What about 60 cm? The result: Well, -8.3 dB. Almost the same.

50 cm? -8.2 dB. The same again...

Let's jump directly to 30 cm deep. That gave me -16.9 dB. A huge improvement!
The desk was 70 cm from the TV. What if I moved it further away from the TV? I tried 5 cm:

Moving the desk just 5 cm away from the TV resulted in -21 dB. Yes! So my conclusion is that a depth of 30 cm and a distance of 75 cm from the TV gives me the desired result. Now, what about width? The previous sheet was 90 cm wide.

70 cm wide? That gave me a desk reflection of -14.6 dB.

60 cm wide? -15.9 dB. An improvement.

50 cm wide? -19.9 dB. Yes! Perfect!
So, my conclusion is that the desk could be 30 cm deep and 75 cm away from the TV, and 50 cm wide otherwise. In theory, this design would work:

Here it is in real life.

The result: -16 dB. What! Acoustics can be counterintuitive sometimes. After speaking with Jens, I realized it's not that simple. The sound perceives the entire surface. He recommended a surface with slats. I couldn't make that since I don't have a jigsaw.

I guess -16 dB is ok. And the size is ok.
But I didn't really give up. After more research I saw someone recommending a perforated surface. That, I could do:

I drilled holes according to a report called "The_Acoustical_Uses_of_Perforated_Metals_Handbook.pdf." They used a thin metal sheet, not plywood, but maybe it would work anyway?

The result: -18.1 dB. Better!

Ok! I bought a jigsaw... I really wanted to try slats. After drilling holes, I drew lines to form the slats. The slats were angled 60 degrees. This is a sheet of 39.5 cm x 90 cm. I found a foldable stand that was 39.5 cm deep.
https://www.thomann.de/se/km_18950.htm

The resulting desk.

The result: -20.6 dB. Yes! Finally!
Well, that was a journey! Next up, I plan to mount the TV on the wall. Currently, it's 20 cm into the room, which should help with super early reflections, maybe? After that, I'll experiment with different monitors! More on that... in the next post!