Here's a pretty comprehensive list of bike headlights, their output, cost, and a their specifications https://www.bikelightdatabase.com/headlights/ Unfortunately the listing does not include any references to the many bright, inexpensive, and rugged headlights available from international sellers. Sometimes it is the same light with a US seller's brand added at double or more of the cost.

Here's an example of one I got for a birthday gift recently. It's a Blitzu Gator 320 (320 lumens, USB rechargeable) which cost her about $30 on Amazon. The exact same light can be purchased on eBay without the Blitzu name for $10.42 postpaid from China. I didn't have the heart to tell her that it was only 1/3 as bright as the single CREE XML-T6 flashlight that I normally use for a bike headlight.

$28.68 from US seller versus $10.42 here USB Rechargeable 360° Rotation Bike Bicycle Front Lamp Headlight Rear Light Set | eBay Exact same light, both postpaid.

You can find some very nice aluminum housed headlights on eBay with from one to five CREE emitters. CREE lists the output for the XML-T6 as 1000 lumens at 1W. I own both a single and 5 emitter lights. The 5 CREE light is incredibly bright. They run on an 8.4V Li-ion battery pack. The brighter the light, the shorter the run time for the same capacity battery. I really prefer this type of light over the Blitzu light with an internal battery as the battery capacity is much greater for the separate battery model. Check out the cost for just a battery for some of the lights made by Nightrider. The battery alone is twice the cost of the Chinese light.

Here are two like the ones I own:
5 CREE Light (really 5000 lumens) $27 postpaid from US seller 5 x Cree XML T6 LED 10000 Lm Bike Bicycle Rechargeable Light Headlamp Torch Lamp 5 x CREE XML T6 LED 10000 LM Bike Bicycle Rechargeable Light Headlamp Torch Lamp | eBay (light, battery pack, and charging unit) and a single CREE (really 1000 lumen) headlight (light only) $9 postpaid 3000 Lumen 3 Mode Cree XML T6 USB LED Headlamp Bike Bicycle Light Headlight 3000 Lumen 3 Mode CREE XML T6 USB LED Headlamp Bike Bicycle Light Headlight Lot | eBay or buy with battery pack $17 2500Lm CREE XM-L T6 LED Cycling Head Front Headlamp Bicycle Bike HeadLight Light 2500LM CREE XM L T6 LED Cycling Head Front Headlamp Bicycle Bike Headlight Light 508966664033 | eBay