File tree diff: cache diff result

[stsewd]

What's the problem this feature will solve?

Since we are using just some sets operations over the files to get the diff, I don't think the operation itself is expensive. Probably it takes more time to fetch the manifests from storage.

Describe the solution you'd like

We can cache the result, probably this isn't relevant to .org, since the response from the addons is always cached. On .com we could cache the result so it's relevant for private docs.

Alternative solutions

Do nothing, getting the diff should be fast enough?

Additional context

#11646