Before the current engagement craze that had overtaken social media companies, spearheaded by Facebook, websites used to send useful emails. For example, if you had received a message in their platform, the message itself was part of the email. (A notable exception is Slack, that still makes itself useful.)
Over time, this functionality has been removed and all we get is an email that says "you received a message from XYZ, log into our platform so our data scientists can ambush you with tons of distracting information and your morning be gone". This is of course, undesirable.
The idea would be run a server that keeps a headless chrome or similar browser, monitors for messages in the target social media sites and fires emails containing the key information as they arrive.
Automatizing access to websites is a lot of work and it has to be changed every time the target site changes. But success on YouTube alternative front-ends can give some hope in the space.