Sims 4 - on mute after headphones unplugged

I'd try seeing if there are any newer sound drivers.

If you have sound software specific to your audio (something other than windows managment) you can try disabling that software.

Conversely if there is extra software available that you don't use for the sound drivers, you could try installing/enabling it.

If it's a desktop, try using the back 3.5mm jacks and not the front panel jacks.

You could try uninstalling the sound drivers they are already current and reinstall them.

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If it all fails to make it work more "automatic", instead of restarting the game you could try minimizing and use the Playback Devices from window's sound manager.  It might be able to get the sound back working without restarting the game.