At the risk of boring the (bleep) out of some folks...
LEDs are best driven by controlled current - it's common to drive them with controlled (or battery) voltage through a resistor, but that falls off ideal in many ways, especially as the battery voltage changes.
There are now many good LED driver chips in the market (well, who knows in the market of the moment with weird shortages due to pandemic, but generally...) and there are quite a few "flashlight-oriented" ones that include a boost converter so that 1.5 or 3V batteries can drive a 4-5 volt LED. But the volts are not fixed (in the good chips) - the amps are, and the voltage is "as needed to produce the "safe but effective amps" for best light output without frying the LED. Among other tricks, the voltage required to drive a current through the LED changes as the temperature does, in a way that promotes "thermal runaway" (it gets hot, it draws more current, it gets hotter, it draws more current, it fries and goes dark) if you use a dumb driver arrangement too close to the limits.
And Rockhewer is exactly correct that the coupling (either by polishing to have a removable LED, or if you're really confident in your LED life, via epoxy) makes a big difference to the output.
Due to the flashlight market, there are a TON of really high output (like, blindingly) battery driven LED packages out there. And plenty of cheap crappy stuff still in circulation, as well as eBay - "failed quality control? - that doesn't me we throw it away, we just sell it on eBay" parts as well. Not the only kind of parts you might find on eBay, but not to be ignored. Some of the non-DOT rated (...cheap) headlight replacements have lower range voltage that will light on a 9V, but I wouldn't bet on the 9V lasting long. But they are bright.
Depending on your driver, jacking up the voltage supply can be a short trip to dark-land.