How can I automatically download the files into my own folders?

The webhook hands you direct download links (media_urls). How you pull them into folders is up to you, but a word on file sizes first: a recording's media files are large, a combined backup can be hundreds of MB, and many no-code “upload to cloud storage” steps have file-size limits (for example, Zapier's Dropbox action caps around 100 MB, and some actions far lower). Routing a full recording through an automation tool into Dropbox or Drive often won't work.

Most reliable (any size): a small script (Python, a Node function, etc.) that downloads the URLs straight into a local or network folder, with no middleman and no size limit. Trigger it from the webhook, or run it on an always-on machine that reads the URLs from wherever you track jobs.

No-code, within limits: Zapier, Make, and n8n work well for the small files (the notes and transcript), and for media only if your destination pulls from the URL directly (its own API, a cloud function, a tool like rclone) rather than passing the file through the automation tool.

Bridge from your existing tools: if your order- or project-management software can hold the URLs, fetch from there. For example, a Google Sheet of links plus a script that pulls each job's files into the right folder.