VideoPress: Unexpected privacy behaviour for duplicated videos

### Impacted plugin

Jetpack

### Steps to Reproduce

1. Enable VideoPress (Jetpack version 10.9)
2. Enable site wide video privacy
3. Upload a video to a page via wp-admin using the Video block
4. Set the privacy level to site default
5. Add the same video in a separate block
6. Set the privacy level to public
7. View the post on the front-end, logged out
8. You will likely see both videos appearing as private
9. Try multiple combinations of video privacy - the front-end behaviour remains unexpected and appears to be influenced by what the previous video settings were

Reported during internal testing: p8oabR-QB-p2#comment-6202

### A clear and concise description of what you expected to happen.

Though this seems more of an edge case, it's possible that there are use-cases for adding multiples of the same video to a post or page. If adding the same video to the page multiple times, I'd expect the selected video privacy for each video to match what is set.

### What actually happened

_No response_

### Other information

_No response_

### Operating System

macOS

### OS Version

12.1

### Browser

Chrome/Chromium

### Browser Version(s)

100

Reproduce the issue in Jetpack 10.9 with VideoPress, site-wide privacy enabled, and two Video blocks referencing the same video with different privacy settings. Start by tracing how each block's selected privacy is handled when the post is viewed logged out. Done means each duplicated video follows its own selected privacy level across the combinations described.

Written by the indexing model from the issue text.