Arduino. Google how to make a voltmeter. 30K/12K resistors should be good. You don't need over voltage protection in this case for the voltmeter.Ok where would to put this relay and how to wire it up?
Your voltmeter will go to the dome lamps. If your Arduino detects a PWM signal then turn your leds on.
Tie into one of the 5V PWM dash LEDs. Plug that directly into the Arduino and again read PWM. Use this to get reference for dimming via the OEM dimmer.
The Arduino itself should be able to power a substantial amount of LEDs but if you are going crazy you will need a separate power supply.
Power itself should come from any RAP circuit. I would use 5V hardwiring kits made for dash cams as those are cheap and work well enough.