I found the solution. The issue was that Salesforce CPQ creates the quote document on Quote Documents and Notes/Attachments whereas the DocuSign is expecting the document in the Files associated with the Quote.
Solution: Create quote documents on Files as well
How: Enable “Post to Feed”
Steps:
Enable Chatter on your quote objects
- Navigate to Setup | Feature Setting | Chatter | Feed Tracking
- Choose Quote.
- Click the Enable Feed Tracking checkbox.
- Click Save.
Change Where the Quote Document is Attached
- Navigate to Setup | Installed Packages.
- Click Configure next to your Salesforce CPQ Installed Package.
- Locate the Document tab.
- Choose Quote as the Attachment Target.
- Click the Post to Feed? checkbox.
- Click Save.
Link: https://help.salesforce.com/s/articleView?id=000380561&type=1