Remove async_trait from the Handler trait

[arpad-m]

Newest attempt to remove async_trait from the Handler trait.

Earlier attempts were in #7301 and #8296 .

[github-actions]

3883 tests run: 3768 passed, 1 failed, 114 skipped (full report)

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Failures on Postgres 15

• test_storage_controller_heartbeats[failure4]: release-x86-64

# Run all failed tests locally:
scripts/pytest -vv -n $(nproc) -k "test_storage_controller_heartbeats[release-pg15-failure4]"

Flaky tests (4)

Postgres 16

• test_ondemand_wal_download_in_replication_slot_funcs: release-x86-64
• test_scrubber_physical_gc[4]: release-arm64

Postgres 15

• test_scrubber_physical_gc[4]: release-arm64
• test_subscriber_restart: release-x86-64

Code coverage* (full report)

• functions: 31.7% (7342 of 23149 functions)
• lines: 50.0% (59471 of 119018 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
6136cf6 at 2024-09-08T12:36:53.560Z :recycle:}