I use a T420 and besides needing to do a bit of configuration in Arch (just needed to check keybindings in i3wm and install PulseAudio) it works exactly how OP

I use a T420 and besides needing to do a bit of configuration in Arch (just needed to check keybindings in i3wm and install PulseAudio) it works exactly how OP would want - though it's in software, not hardware (so if you use console a lot things will get ugly). I press the mute button, it's muted. I plug a headset into the audio jack, it remembers my previous settings. I'll be using this computer until time pries it away from my fingers. Edit: forgot to mention, it has a physical microphone button too. It's just amazing for Discord and Zoom calls.