Were you able to make it work? I'm facing similar issue with Apple Mail app. I'm getting the prompt that I've attached and the log says "systemSharingUIDidSaveShareBlock received error: <CKError 0x2801d9500: "Permission Failure" (10/2007); server message = "Invalid bundle ID for container"; op = 33F7539C6A16E928; uuid = DF53ACF4-73AE-4763-947E-2A3FA7E4F241; container ID = "iCloud.my.container.id">". This only happens with Apple mail. other options like Messages, Gmail and Link sharing "Invite with link" work. Sharing with Apple mail stopped working after upgrading to iOS 16.

I'm facing the same dilemma. What did you end up using?