Beeper is a bunch of Matrix bridges run as a commercial service. You can join the wait list or set up your own Matrix+bridges if you want (though that's more fiddling around).
As Beeper is based on Matrix, you can use the standard Matrix API, use libraries like Maubot, and plenty of others in other programming languages. HTTP calls are one way to send/receive messages but there's more flexibility to be gained if you pick a wrapper library IMO.
Not sure about other chat apps, but to connect to imessage they were originally using jailbroken iphones and now use MacOS virtual machines, according to another commentator. So there is a bit of additional work that would be necessary to fully replicate it.
Disappointing, but iMessage has always been Apple's special little protocol nobody else can use.
Still, there are Docker images out there (that break the TOS) for running macOS inside QEMU, I'm sure someone can script one of those to set up a bridge more easily?
As Beeper is based on Matrix, you can use the standard Matrix API, use libraries like Maubot, and plenty of others in other programming languages. HTTP calls are one way to send/receive messages but there's more flexibility to be gained if you pick a wrapper library IMO.