That makes sense in the case where people are mindfully connecting with particular individuals or organizations, and paying for that.

Not for where algorithms select media for you. That's not a "networking service", even if that is one of its hooks. Unless you consider SPAM or junk mail, riding on email and postal "networking" to be a "service".

"Attention media" is more accurate.

But that also describes traditional advertisement based "media". Which earned its keep via attention access, by including unintegrated ads as a recognizable second component.

A description specific to the new form is "surveillance/manipulation media" or "SM media".

Attention-access funded media lacked pervasive unpermissioned surveillance and seamlessly integrated individualized manipulation. Where dossier-leveraged manipulation, not simply attention access, has become the defining product.