The client is interested in whether they need to purchase an Extended license for videos with monetization on YouTube?
“I would like to use it as intro to all my Youtube videos (including monetization)…Do I buy the single regular license without getting a copyright strike?”
yes, deciding factor is that it is free to watch for the end user (the viewer). As long as the video is not behind a paywall a regular license is fine.
free to watch does not mean non-commercial. Youtube is free to watch (wit hthe exception of the premium youtube red) and yet many people are earning money with monetization.