VideoPress: module is still activated when downgrading plan

#### Steps to reproduce the issue

0. Start from a Jetpack site with an active Premium upgrade.
1. Go to Jetpack > Settings, and enable the VideoPress feature.
2. Remove the Premium upgrade from your account.
3. Go to Media > Library.
4. Upload a new video.

#### What I expected

Video should be uploaded correctly and not processed by VideoPress.

#### What happened instead

VideoPress intercepted the upload, but the video is not uploaded, probably because the API detects that we're missing an upgrade.

#### Additional info

We found this when testing https://github.com/Automattic/jetpack/pull/11193 (props to @dmsnell).

I noted that Jetpack loads the `/modules/videopress.php` file when we downgrade from Premium to Free. Furthermore, this stops happening as soon as you visit "Jetpack > Settings", so it seems that the VideoPress module is not deactivated during the downgrade, and we deactivate it when visiting the "Jetpack > Settings" page.

Reproduce the downgrade flow from the issue, then inspect modules/videopress.php and the module lifecycle around the plan change. Confirm that downgrading from Premium prevents VideoPress from intercepting new uploads, including before visiting Jetpack > Settings.

Written by the indexing model from the issue text.