(written from a Production point of view)
The Starfleet Internet was mentioned in material created for the Picard family album, which did not make it on-screen.
In 2327, the family members of cadets from the class of 2327 were invited by the Trustees of Starfleet Academy to a graduation ceremony at Starfleet Academy. The invitees were asked to RSVP through the Starfleet Internet.
On the invite, Internet is misspelled as "Intrernet".