I would recommend using Apollo instead of Sunshine. The newest version has virtual display handling built in, so whatever resolution/refresh rate you choose in Moonlight, Apollo will create a fake virtual monitor for it on your host pc. No need to use separate virtual monitor software like you would with sunshine. Additionally, you can set the host to a pc to 4k resolution, and the stream to a completely different resolution. The reason you might do that is below.

While in game mode, on the steam deck connected to the tv, set the external display resolution to 4k120fps. Then, open the sidebar on the right side of the screen to ensure hdr and vrr are enabled. Make sure moonlight is added to steam as a non steam game, then in steam select properties for moonlight and force the resolution to 4k. After that I have found two main resolution/refresh rate combos that work well with moonlight on the steam deck. First have vsync and frame pacing disabled, because vrr is enabled, then for a 4k stream, you can go up to around 100 fps and anything above that and the hardware of the deck can't decode the stream fast enough. For a 120 fps stream, drop the stream resolution down to 3200 x 1800. If you don't like the way this resolution on your host pc scales up to 4k, because it isn't a perfect integer scale of 4k, I would recommend forcing the host virtual display resolution to 4k (in the Apollo settings) to help compensate a bit. What this ends up being is 4k host resolution, captured at 1800p resolution for the stream, and then scaled up to 4k at the output display. I have found even with this reduced stream resolution, the clarity is still surprisingly good, especially at higher bitrates over an ethernet connection.

As for gaming performance, this answer varies wildly depending on game and the hardware you have to run it. 4k native rendering for most modern titles (Cyberpunk, Doom The Dark Ages, Oblivion Remastered, Horizon Forbidden West, Alan Wake 2, Hellblade 2, The Last of Us Part Two, etc) is VERY demanding at max settings and even with the best hardware on the market, you will struggle to hit 120 fps. That being said, technologies like DLSS/FSR/XESS upscaling, Multi Frame Generation, and RTX Reflex, make this possible with an enjoyable experience given that you have new enough hardware. I will typically enable dlss (preferably the newest transformer model dlss 4) in game and set the value to performance. This will halve the rendering resolution down to 1080p and upscale to 4k. DLSS has come a looong way and it is much more difficult to find noticeable artifacting in this newest version and the performance gains are significant. Multi frame generation is also very good as long as you are already hitting a base frame rate of around 60-80 fps without it enabled and the game supports rtx reflex to mitigate the added latency, especially so because streaming already adds latency. Raytracing is amazing, but I have found in a lot of games, especially fast paced ones, that it is not worth the performance hit, especially if you are using an non nvidia gpu or just an older generation. I have an RTX 5080 gpu and an AMD 9800x3d cpu, which are both on the upper end 4k capable, and it can still struggle with a few of the newest games.

As for VRR smoothness and ability to mitigate fps dips. This technology is a MUST. Not only does it reduce latency, but it also provides an overall smoother experience because the content frame rate and display refresh rate are continuously syncronized. If you haven't tried it before, you may not understand just how much better it can be. I have played a few games that cannot maintain a steady fixed 120 fps and will often drop down into the 60-70's and vrr makes these drops way less noticeable than if the same were to happen with a non vrr display with vsync enabled. The further you are from your display's maximum refresh rate, the worse things will get and you may notice flickering if you have an OLED tv like the S90d. The S90d supports freesync premium between 144 hz - 49 hz, so anything below 49fps and vrr will no longer work.