If Chirpstack is working the API is working, no extra installs necessary. The endpoint is the same DNS as your web UI, including port. The API protocol documentation can be found here: Protocol documentation - ChirpStack open-source LoRaWAN® Network Server documentation.
I don’t know much about PHP but I use python for the gRPC API, here are some examples I’ve given to others: Creating Channel and Retrieving Metrics, Activating a device, Retrieving Keys.