Python

VPN server on one, client on another.

A matrix bot on each end would work too but seems unnecessarily complicated.

The easiest & cheapest option would be to expose one of the devices to the internet on a known port and connect from the other device to that one with SSH.

Once you've got a connection, you can do pretty much anything you want, including writing to a pipe or even a file and polling it.

If you don't want to expose either, then you need a third party to facilitate the connection that is on the Open internet, though that server can be yours too. Even a €4/mo box at Hetzner would do it.

If these options sound good, let me know and I can be more detailed.

For a simple one way communucation where latency is unimportant, you might leverage any number of free services with apis you can abuse. You could send a tweer, or nastodon message, You could have one just update a file with a timestamp as a github gist or on pastebin or something.

There are also free mqtt broker services.

Or you could put one on the public internet with ddns name and talk directly to it.

Or you could set up a VPN between them - is logmein still a thing? - and then talk to each other directly via that interface