Does anyone know:
-is a fire more likely when the device is on? (I turn mine off, vs sleep, as much as possible - thinking it might help)
-is a fire more likely when charging? (I try to avoid using my portable lipo battery pack to charge devices while airborne)
Overcharging due to crappy battery voltage and temperature monitoring in the charger/battery pack design. Internal short circuits due to battery quality issues, vibration, or impact. Those would likely be the biggest causes.
Most big name consumer stuff is pretty safe. The massive liability drives good engineering design and charging circuits. I'd be more worried about charging your no-name lipo pack than using it to charge a Garmin or iPhone.
(That said, LG manufacturing defects caused GM to recall every single Bolt ever made. Combination of both a torn Anode pad and a folded internal separator during LG manufacturing allowed later short circuits to occur).
My thoughts for what it's worth:
I'd never let a vape pen on the plane. I'd be very hesitant with high power density toys like scooters and hover-boards. I'd also never leave either of those on a charger in the house when I wasn't around.
I'd be careful about letting my other battery devices end up where they can be smashed by a sliding seat track or reclining seat back, for example.
Thermal runaway occurs after the battery reaches 400 degrees Fahrenheit or so. You want to prevent that from happening. If I saw something start to smoke, I'd toss it out the window. The likelihood of a small device causing a fire or damage on the ground is way less than a burning plane hitting the ground at high velocity.
Other than that, I have no problem leaving my phone, iPad, GPS, and ADS-B devices on and charging during flight.
YMMV.