page_service: getpage batching: refactor & minor fixes

[problame]

This PR refactors the page_service server-side batching code that was recently added in
#9377.

Changes:

• Store carried-over batching state in a local variable inside handle_pagestream, instead of in the PageServerHandler. This adds robustness because it systematically avoids a source of bugs.
• Instead of next_batch, call it carry.
• When starting a new batch read, take into account the time carried over from the previous call.
• Build the batch inside the &mut Option<Carry> of in a local variable.
  • Before, we would have to make sure that we move the batch back into the self.next_batch whenever we bail.

[github-actions]

5535 tests run: 5309 passed, 0 failed, 226 skipped (full report)

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Flaky tests (1)

Postgres 15

• test_pull_timeline[True]: release-arm64

Code coverage* (full report)

• functions: 31.4% (7951 of 25322 functions)
• lines: 49.3% (63084 of 127831 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
058b35f at 2024-11-21T11:30:41.601Z :recycle:}

[VladLazar]

Checked it out locally and stepped through it a number of times. Looks correct, but have a look at the comments.