Curate, connect, and discover
I headcanon that despite being a shy person in general, and a little anxious when talking to people he doesn't know, Luigi loves oral storytelling.
At the end of Mario & Luigi: Superstar Saga, Luigi is shown talking on the plane ride home, eliciting laughter from everyone around him.
In Super Paper Mario: The Thousand Year Door, Luigi regales his brother with stories about his adventures whenever you talk to him at Rogueport. Even though Mario and his companion will fall asleep while the story is told, Luigi seems to pay no mind and continue unhindered, (and apparently it was interesting enough for a journalist to be drawn in and spin the story into a bestselling book, so there's that.)
On a quiz on the official Play Nintendo Website, Luigi is listed as a good candidate to speak at a graduation because "he'd probably tell great ghost stories."
And in Super Mario RPG, Luigi is the one who guides the player through the manual, and subsequently is the one who recounts the events of the first scene in story format.
I think if he's comfortable enough around you to talk freely, he'll immediately shift into audiobook mode upon request.