To fix open protontricks and select your copy of Fallout 4.
Select the default wineprefix => Install a Windows DLL or component
In the list of dll files, search for faudio and xact. Press OK and allow them to install.
This also works for Fallout 76, except you only need to install faudio for it.
Modding with Vortex installed via SteamTinkerLaunch is not possible, I've personally tried everything and searched everywhere. There is no fix as far as I'm aware.
UPDATE: I HAVE FOUND A WAY TO MAKE MODS WORK WITH VORTEX. READ HERE
There are 2 alternatives, Bottles, to download another version of Vortex. Or Limo, for a more manual experience. I cannot vouch for the Bottles method, as I have no attempted to use it, however Limo is a great alternative that only requires a bit of work to get functioning.