fix(pageserver): categorize client error in basebackup metrics

[skyzh]

Problem

We separated client error from basebackup error log lines in #7523, but we didn't do anything for the metrics. In this patch, we fixed it.

ref #8970

Summary of changes

We use the same criteria as in log_query_error producing an info line (instead of error) for the metrics. We added a client_error category for the basebackup query time metrics.

Checklist before requesting a review

• I have performed a self-review of my code.
• If it is a core feature, I have added thorough tests.
• Do we need to implement analytics? if so did you add the relevant metrics to the dashboard?
• If this PR requires public announcement, mark it with /release-notes label and add several sentences in this section.

Checklist before merging

• Do not forget to reformat commit message to not include the above checklist

[github-actions]

4986 tests run: 4822 passed, 0 failed, 164 skipped (full report)

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Flaky tests (4)

Postgres 17

• test_delete_timeline_client_hangup: debug-x86-64

Postgres 15

• test_subscriber_restart: release-arm64

Postgres 14

• test_ondemand_wal_download_in_replication_slot_funcs: release-x86-64, release-arm64

Code coverage* (full report)

• functions: 32.1% (7469 of 23243 functions)
• lines: 50.0% (60205 of 120510 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
b9d98eb at 2024-09-24T16:39:27.732Z :recycle:}

[problame]

After shipping this, the 4GS dashboard (and alerts? and SLO definition?) needs adjustements.