Did this start right away after the update?
Does it make a difference if the Switch is docked or not?
Did you try changing the voice / dialog volume in the options?
If you start a new game, is there voice acting in character creation if you listen to the origin backgrounds, or in game with the initial dialog?
Moving a bit from the initial character position can trigger an auto save, which might overwrite one from your current playthrough. If you don't already have an honour mode difficulty save, starting one would avoid that problem, since it uses a separate, single save slot (though you don't need to move from the initial position to check voices).
If you start the game from a different user account, if available, do you get the voice acting?
Try clearing the system cache: in the Home menu open System Settings, then select System, Formatting Options, Clear Cache and then the current user.
Note that this will also reset the system language and brightness setting.