What is a typical quote for a 3 minute youtube style video - shot and edited?

Standard answer - you charge what the market will bear. This is based on several criteria, not the least of which is where you live and how much competition there is in said area. Add to that your professional portfolio. Do you have a body of work that supports charging good money or are just a guy with a camera and Adobe subscription? If the latter then you need to go to cheap as you build your history.

Not sure you can define a “typical” YouTube video. If someone asked me to do a “typical” YouTube video I would have no idea what they mean and would have to ask a lot of questions to determine if that video is a promotional, sales, informational, teaser, sizzle or any numerous types of videos.

What is their distribution strategy?

From there it comes to determining the best way to communicate that message - what style of video is best.

Who is writing the script? Me or them?

Then honing that down to what the budget will accommodate.

Interview Talking Head with Music Titles $500 US Half Day Shoot Half Day Post and editing
Promotion Video with AB Roll, Narration, Titles 1 day Shoot 1 Day Post Production and Editing Between $1000 - $1500 US