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You need a Mac or Linux box with internet connectivity with a domain pointed to it (You probably could do it using dynamic DNS too.) I don’t know how much power it needs, you might be able to get away with something like a Raspberry Pi.
You can either run it on your own hardware, or host a server with something like Digital Ocean Droplet, A2 Hosting, AWS, Azure, etc.
You would have to use the Open Source Matrix clients like Element or SchildiChat instead of the actual Beeper App, but you would be able to use the Beeper bridges.
And this would require it be a Mac for iMessage functionality, no?
Probably.