I duckduckgoed “SOT23-6 boost converter” and found a picture of an IC with similar markings - I’m now pretty sure the component is an FP6291 switching regulator by Advanced Analog Electronics.

If you look at the datasheet, the “AL” identifies the part, and the following numbers are the year of production and the wafer lot number, so they could really be anything. The pinout matches as well, given a few inaccuracies in your schematic, which I think I can confirm on the images. Thanks for the image of the PCB against the light, that was very helpful. Pin 1 would be on the bottom right, connected to the inductor L1 to boost the voltage, with the other pins arranged counter-clockwise. Pin 2 should then be connected to your PCB ground; to confirm, you could use a multimeter in continuity mode to measure to the BAT- and 5- connections. The right side of R4 should also be connected to ground, and 24 kΩ would set the current limit of the IC to 2A (page 7). On pin three is one of the mistakes in your schematic as far as I can tell, I think that pin is really connected to the point between R6 and R5, for output voltage feedback. I also think R6 is meant to read “84D”, which would be the resistor code for 732 kΩ with 1% tolerance. If you calculate the output voltage of the regulator with the 0.6V feedback voltage from the datasheet and 732k/100k resistors, it comes out to 4.99V, which would be compatible with the USB 5+/5- stuff. Connecting EN to VCC (pin 4 to 5) is also common to permanently enable an IC, but I think there’s another error in your schematic: I’m pretty sure those two pins are directly connected to BAT+ instead of through C4, and that C4 instead connects from those two pins to ground to stabilize the input voltage.