Rewind: remote calls on admin page load every 10 minutes

When you use the VaultPress plugin, we run a check on every admin page load to see if the VaultPress submenu should be displayed:
https://github.com/Automattic/jetpack/blob/6.1/3rd-party/vaultpress.php#L31

While this seems harmless, especially since we cache the results of the rewind check for 10 minutes at a time, on some sites the REST API call can take a long time to respond (as reported in 1162372-zen).

It would be nice if we could store that check for a longer period of time, or avoid doing a remote request to find out when a site uses Rewind or not.

Start at 3rd-party/vaultpress.php around line 31 and trace the cached Rewind check and REST API request made during admin page loads. Verify the reported delay, then establish whether a longer-lived check or avoiding the remote request meets the goal without preventing correct VaultPress submenu behavior.

Written by the indexing model from the issue text.