Instead of using the video widget, use custom code.
Generate embed code on Youtube on a given video. Take notice of where the ID of the video appears in the code.
Create a Collection called "home video" and inside put a text field for the youtube ID. Create a post and put the video ID.
In webflow, inside a Dynamic list, put a custom code widget, and paste your youtube code inside.
Select the ID in the code and click on the upper left corner of the dialog box where you can like to a collection.
target the link to the video collection and ID text field
Now you cans setup your dyn list to only show the last post (1 post starting to 1).
Each time your client will add a new video, it will replace the one on home.
Surely can be done with playlists and playlists IDs.