Remove async_trait usages from safekeeper and neon_local

[arpad-m]

Removes additional async_trait usages from safekeeper and neon_local.

Also removes now redundant dependencies of the async_trait crate.

cc earlier work: #6305, #6464, #7303, #7342, #7212, #8296

[github-actions]

3801 tests run: 3695 passed, 0 failed, 106 skipped (full report)

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Flaky tests (5)

Postgres 16

• test_lfc_resize: debug-x86-64
• test_cancellations: debug-x86-64
• test_subscriber_restart: release-x86-64

Postgres 14

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

Code coverage* (full report)

• functions: 32.5% (7413 of 22799 functions)
• lines: 50.7% (60168 of 118671 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
83eaeae at 2024-08-29T14:08:13.522Z :recycle:}