OTel: Use async batch span processing and Tokio runtime

[cloneable]

Problem

Summary of changes

[github-actions]

8910 tests run: 8246 passed, 0 failed, 664 skipped (full report)

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Flaky tests (4)

Postgres 17

• test_compute_pageserver_connection_stress: debug-x86-64-without-lfc
• test_hot_standby_gc[True]: release-x86-64-without-lfc

Postgres 15

• test_hot_standby_gc[True]: release-x86-64-with-lfc
• test_ps_unavailable_after_delete[DeletionAPIKind.FORCE]: release-x86-64-with-lfc

Code coverage* (full report)

• functions: 34.8% (8798 of 25291 functions)
• lines: 45.9% (71106 of 154872 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
a72ced5 at 2025-07-22T20:56:11.792Z :recycle:}