You have already found the only official control, so let me be straight about what is and is not possible and then give you the practical answers people actually use.
On a PS5, the light bar brightness setting is the full extent of the official control. There is no off. Setting it to the dimmest option is a real reduction and worth doing, but as you have noticed it remains visible, especially reflecting off a screen in a dark room. The player indicator LEDs above the touchpad are covered by the same brightness setting.
So the practical options. The one most people settle on is a small piece of matte black electrical tape, or a strip of thin craft felt, over the light bar. It is completely reversible, it does not block anything functional, and it removes the reflection entirely. Choose matte rather than glossy tape, since glossy still reflects. Some people use a thin strip of dark translucent film instead, which dims rather than blocks and keeps the charge indicator readable, which is the one thing you lose by blocking it fully: the light bar is how you see that the controller is charging.
On a PC the situation is different and worth knowing. Windows sends no lighting instruction, so on a PC the light bar typically sits at a default and third party software can control it directly, including turning it off, because lighting control is available over USB. So if your distraction is mainly during PC use, software is a real option there in a way it is not on the console.
On battery: yes, dimming gives a genuine but modest gain. In our testing the difference between brightest and dimmest was in the region of five percent of runtime. Noticeable over a long session, not transformative, and a good reason to dim it regardless of the reflection.
