This document is most likely incomplete, because my knowledge is too. Some stuff is probably wrong too.
I will not list what I consider to be general linux knowledge here, just stuff that applies to this exact use case.
Audio Device -> JACK -> ASIO (wineASIO) -> RS_ASIO -> Rocksmith2014
Rocksmith usually uses WASAPI for audio input and output.
For pro-audio, which is used for music production, there's an audio system called ASIO on Windows.
Linux has 4 sound servers/systems: ALSA, pulseaudio, pipewire and JACK. JACK is for pro-audio. Pipewire is quite new and aims to be the one standard for all, which is why it has implementations for all of the other ones.
JACK and ASIO are equivalents. Since there's Wine and some people want to do music production on Linux, there's wineasio, which translates between these.
Someone developed RS_ASIO, which you could say is a mod for Rocksmith to work with ASIO devices.
Plugging everything together, we get the chain above.
You install JACK and set it up in a certain way. You install wineasio into the standard wine, as well as your runner (Steam Proton, or something else you use). You patch the wine prefix to accept WineASIO and install RS_ASIO to Rocksmith.
Steam Proton has a wrapper, which contains libraries and files that are used instead of system files, to ensure that the games work the same across every platform. Somehow, this destroys functionality with WineASIO. In the past, we tried to start Rocksmith without the wrapper. This isn't possible anymore because of an update to the game.
I don't know why exactly the script works, but not the "Play" button in Steam, but it does.
YES!
The only reason that Rocksmith takes ASIO is because of RS_ASIO. Once you remove that mod (eg. append ".bak" at the end of all the files), you're back to WASAPI and can use the quick and dirty method.
(Come to think of it, you have to select input and output device in winecfg, but I don't think it should make a difference.)