Diary entries are stored in the page itself, as a table inside the macro. That single design decision is what gives you everything on this page for free.
Search
Entries are page content, so Confluence indexes them. Searching for words you wrote in an entry finds the page that holds it - there is no separate app search to learn, and no Diary content that Confluence search cannot see.
Page history
Every Diary entry you add, edit, or delete creates a new page version, with a version comment saying what happened and quoting the beginning of the entry:
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New Diary entry: …
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Edited Diary entry: …
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Deleted Diary entry: …
So page history reads as a log of the Diary - and a deleted entry is never really gone. Revert the page to an earlier version to bring it back.
Because each change is its own page version, a busy diary produces a lot of versions. That is expected, and it works the same way on Data Center.
PDF and Word export
Exporting the page to PDF or to Word carries the entries table - the dates, times, authors, and content - and nothing else the macro body happens to hold. Viewing the page shows only the entries too, so nothing a reader could otherwise see is lost in the export.
The same rendering is used when you compare two page versions in page history.
Backups and audit
There is no separate app data store to back up. Whatever you already do to back up, archive, or audit Confluence pages already covers every Diary entry, because the entries are page content.