Can I power multiple devices from one output of a power supply?
Yeah, this will work, however:
Better get a good quality power supply (brands like Meanwell) than no-name junk. These individually addressable LEDs draw current pulses. Some cheap power supplies have trouble regulating the voltage, or they will emit audible whine, which is annoying. Some junk brands are quite dangerous and omit stuff you really want to have, like proper creepage distance between primary and secondary, or proper fusing, or filtering, or proper cooling. It isn't worth risking fire or electric shock to save ten bucks on a power supply. Also a good quality supply will be more efficient, so you can be proud to Save The Planet™.
If you use a power supply that is quite powerful, like 16A, then you need to make sure the wires you use won't melt and cause a fire in case there is a short somewhere. Better pick a power supply with hiccup overcurrent protection that will shut down in case there is a short and periodically try to restart, rather than a dumb power supply that will just use a current-limit and sustain 16A through your wires.
You will connect ESP32 ground to LED ground, and both grounds to power supply. Make sure this connection is absolutely solid. If the LED ground gets disconnected from the supply, but ESP32 ground remains connected to supply and LED, then the full LED current would go through ESP32 PCB, which means bad news. Basically, this is a possibility if your ground wires make a triangle.
Keep wiring short, clean, and twisted. ESP32 emits quite fast signals to control the LEDs (I'm assuming something like WS2812) so you should twist that wire with the LED ground and supply. If the control wire makes a large loop it will have extra inductance, signal integrity will be bad, and the LEDs won't get proper commands.
Put a 2A polyswitch or fuse on the USB ports. If the USB cable gets damaged through repeated bending and has an internal short, you don't want 16A running in it and melting both the connector and the cable.
Also, on the AC mains part, make sure you do it up to code.