imho, the application (in this case Tropico 5) has to be compiled using the new version of Microsoft.XAudio2.
Nuget packages are installed in the development environment (Visual Studio) and the libraries are used in application development afterwards.
Kalypso would have to re-compile Tropico 5 with this new version (given the new version really fixes the issue) and include the distribution of the new Microsoft.XAudio2 dll in the Tropico 5 setup (given it is not deployed automatically as part of a monthly windows 10 cumulative update).

EDIT:
"[...]When the DLL (player100: the redistributable dll from the nuget package) is used on a Windows 10 system, it checks the version number of the XAUDIO2_9.DLL that is part of the operating system, and if the operating system is newer, it will delegate all API calls to XAUDIO2_9.DLL in the operating system. This ensures that apps always use the latest version of XAudio 2.9 that is available on the current platform.[...]"
Source: https://docs.microsoft.com/en-us/windows/win32/xaudio2/xaudio2-redistributable

It is not so clear, could you explain, is it possible to install the defined NuGet package and fix the problem with sound and crashes in Tropico 5, or the Kalipso still needs to recompile the game?

The nuget package is intended for developers. They either include the proper version of the dll with their application or rely on Microsoft to push the newest version of XAudio2_9.dll via monthly cumulative updates for Windows 10 to devices running Windows 10.
Anyway Tropico 5 seems to use XAudio2_7.dll (according to the error logged in Windows event log) and therefor Kalypso would have to recompile it using XAudio2_9.dll. I don't know if this would be easy (just update the reference to the new dll and recompile) or if additional changes to the source code would be required to make it work with the newer dll (because the API changed or something else).

Version history of XAudio2: https://docs.microsoft.com/en-us/windows/win32/xaudio2/xaudio2-versions

Many mobos actually have realtec chips in them. This is also not the first time that there has been a problem with audio unload. The difference then was that it was one of their games so they fixed windows quick. This time they don't have the money incentive to fix what they broke.

Hopefully I don't sound incredibly dumb here, but is there a way of downloading XAudio_7 to the latest version of Windows 10 and putting it in System32 as it would be in previous editions of Windows 10 or am I missing something bigger here?

Hola.
He probado todas las soluciones aquí expuestas y solamente me han servido aquellas que implicaban jugar el juego pero sin sonido.
Al parecer la versión de Steam no tiene este problema, lo he comprobado no comprando el juego sino descargando una versión crackeada.
La única solución valida por el momento creo que es descargar una versión crackeada del juego, si realmente han pagado por el juego no hay ningún problema con eso pues lo malo de la piratería se supone que es jugar juegos sin pagarlos, por lo que creo que quienes hemos comprado el juego estamos en nuestro derecho de jugarlo, aún si significa que sea una versión crackeada.
Si han comprado el juego en GOG y no pueden disfrutarlo, comparto un enlace de un vídeo que soluciona el problema de la manera que detallé arriba.
youtube.com/watch?v=BV2vLgcOuDA

English translation by google translate:

Hi.
I have tried all the solutions presented here and only those that involved playing the game but without sound have helped me.
Apparently the Steam version does not have this problem, i have verified it not buying the game but downloading a cracked version.
The only valid solution at the moment I think is to download a cracked version of the game, if they have really paid for the game there is no problem with that because the bad thing about piracy is supposed to be playing games without paying for them, so I think that Those of us who have bought the game have the right to play it, even if it means that it is a cracked version.
If you have purchased the game on GOG and are unable to enjoy it, I share a link to a video that solves the problem in the way I detailed above.
youtube.com/watch?v=BV2vLgcOuDA

You can download and install an older DirectX runtime via https://www.microsoft.com/en-us/download/details.aspx?id=8109. That should include the XAudio2_7.dll (and even older ones). But it doesn't help, Tropico 5 won't stop to crash after a short period of time.

Yup! Spent my money on that darn game due to GOG's advertising, just to find out that they lured me into a trap! I want my money back! Either a game works or it shouldn't be sold! Seriously, it will be the last time I spent money on GOG, I have had trouble previsously and it seems that it's just business as usual for GOG when titles they sell don't work correctly.

Update, the GOG copy still has this crash issue.

Maybe Win-Update helps. Copy from Steam-Forum:
"Game is working again on Windows 10 2004
I had some problems on Windows 10 1909 due to Xaudio compatibility. But now after updating my Windows, It works again and with Audio. Just a heads up."

Hello,
Game is not working after installing Windows 10 2004 on my computer.

Même problème, impossible de la lancer, la seule solution trouvée et d'utiliser linux et lutris (même si pas de son)

Same problem, I cannot make the game working. The only way, was to use linux and lutris ( I don't have sound :( )

something new about this problem?

Nope, still doesnt work. GoG should remove Tropico 5 from it's catalogue