Answering a technical question

Q: Is there a setting or mode change that would allow me to watch the playlists seamlessly instead of having to click on each individual match after the previous one ended? I don't know why, but this matters to my viewing experience.

A: Yes, this is possible but not using the web version of Google Drive. If you install Google Drive for desktop and play the files from there (you’ll want to create a shortcut to all of it on your own Drive so it actually shows up for you on desktop) and then play the files with VLC player, they can play on a continuous loop.

Open the folder in VLC, add the files to the playlist (or drag them in), and then click the "Loop" button until the icon shows "Loop all" (a circular arrow with a '1' inside or just the arrow for playlist loop), making them play in sequence and repeat.