Damian rarely uses technology for anything outside of contacting people. However, he has been using more often as he navigates his first amorous relationship, though BuzzFeed and Vogue articles remain largely unhelpful when you're dating someone with a... unique personality and very dubious hobbies.
Vincent, on the other hand, has the search history of a writer—questionable, random, and would put him on the FBI watchlist if he wasn't already there. His queries range from, 'How much weight does it take to crush someone's head?' to 'Best farmer's market near me.' Outside of Google, he's largely uninterested in social media and news articles—he prefers the newspaper like an old man. His main phone is his 'work' phone he uses during his night job. It's the number where people contact him for his 'services.'
Thank you for your question! Feel free to ask more; I rarely get to write out these random headcanons outside of my Google Docs!