I've had the best luck with Moonlight (OSS client) and Sunshine (OSS server replacement for GeForce Experience's "GameStream") -- very minimal latency (almost completely undetectable) from my RTX 3090 PC to my Nvidia Shield.
If your server is Linux and you have an NVIDIA card, I would also recommend applying the NVFBC consumer card restriction removal patch[1] to your driver libraries to allow you to capture directly from the GPU rather than X11/Wayland. Sunshine will automatically detect this and use it and it reduces the latency even further.
However, NVIDIA say that "The NvFBC desktop capture library does not have native Wayland support and does not work with Xwayland" (https://us.download.nvidia.com/XFree86/Linux-x86_64/565.77/R...), so I guess it's of no use for Wayland users.
Highly recommended.
Sunshine / Moonlight was also briefly pitched at the end of Arstechnica's coverage of this RPi Steam Link, fwiw. https://arstechnica.com/gaming/2024/12/the-raspberry-pi-5-no...
I switched to using my Steam Deck. Moonlight on a docked Steam Deck with Sunshine works perfectly with HDR on an Ethernet connection. The Steam Deck should also have better controller support than the Nvidia Shield- I've been using the official Xbox wireless adapter, there's a community supported driver to use it with the Steam Deck- a video on Youtube says how to get it working.