Sidebar navigation: Backup item is not showing up

Edit: related issue here: https://github.com/Automattic/jetpack/pull/23532

Noticed a very buggy behavior with the Backup item in the sidebar navigation **that's preventing customers from finding their way to the Backup interface in cloud.jetpack.com**.

### With a Backup plan

- Issue: notice how Backup is not present in the sidebar even though we have an active subscription.
- Expected behavior: show Backup link.

### With a Scan plan

- Issue: It does shows up correctly when we have a Scan subscription.
- Expected behavior: show Scan link.

### With a Security plan

- Issue: In this scenario we should see “Backup & Scan” since we have both products. However, only Scan is visible.
- Expected behavior: display Backup & Scan links.

### With the free plan, upon landing on Jetpack after connection

- Issue: In addition to the use cases above, sometimes even without a subscription, the Scan link is visible in the sidebar.
- Expected behavior: no Scan link should show up.

Relevant code is here:

https://github.com/Automattic/jetpack/blob/2447e267e40f2d133a5c15c2320b776e4c395ec8/projects/plugins/jetpack/modules/scan/class-admin-sidebar-link.php#L60-L84

Start with projects/plugins/jetpack/modules/scan/class-admin-sidebar-link.php around lines 60-84, then compare the sidebar output for Backup, Scan, Security, and free plans described in the issue. Confirm the subscription checks and the related pull request before making changes; done means each plan displays exactly the expected sidebar links and the free plan displays no Scan link.

Written by the indexing model from the issue text.