Meaning of TV Backlight LED strip details
LEDs are like Zener diodes and these 8S3P power LEDs are drawing 84W according to your measurements, so the backplane provides a good reflector of light and radiator of heat dissipation required to operate them with a reasonable warm temperature rise.
You can use the same power supply and possible figure out how to dim the current with some control signal or feedback signal pot as I imagine they are exceptionally bright.
It appears each white LED is very efficient but drawing  3.5W and is composed to 2 series white LEDs in each chip. Thus each string is matched by supplier quality to be only 5.5V per dual LED, which is implies to me they are very efficient with low series resistance at full brightness and very high resistance at the leakage voltage threshold of 39.5V at about &lt;100uA.
That explains to you why the voltage range from off to full brightness has a small range in voltage. They are like very powerful Zener diodes.

What voltage should I input?


same as what you measured up to 44V


Can I dim the light?


only if you can show the interface signal that controls the current then figure how to make that using the same power board repackaged to power the LEDs in a safe manner.


What's the current being used


up to the same as what you measured.