Integrate tracing into Bridged proxy, add BridgedRequest span #23347

[serbel324]

Changelog entry

Support Distributed Storage tracing in configuration with multiple piles

Changelog category

• Improvement

[github-actions]

⚪ 2025-08-22 13:43:17 UTC Pre-commit check linux-x86_64-relwithdebinfo for c866227 has started.
⚪ 2025-08-22 13:43:31 UTC Artifacts will be uploaded here
⚪ 2025-08-22 13:47:12 UTC ya make is running...
🟡 2025-08-22 15:36:57 UTC Some tests failed, follow the links below. Going to retry failed tests...

Test history | Ya make output | Test bloat

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
39488	36737	0	4	2711	36

⚪ 2025-08-22 15:40:33 UTC ya make is running... (failed tests rerun, try 2)
🟢 2025-08-22 15:54:21 UTC Tests successful.

Test history | Ya make output | Test bloat | Test bloat

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
491 (only retried tests)	466	0	0	1	24

🟢 2025-08-22 15:54:29 UTC Build successful.

[github-actions]

⚪ 2025-08-22 13:43:45 UTC Pre-commit check linux-x86_64-release-asan for c866227 has started.
⚪ 2025-08-22 13:43:59 UTC Artifacts will be uploaded here
⚪ 2025-08-22 13:47:50 UTC ya make is running...
🟡 2025-08-22 16:12:41 UTC Some tests failed, follow the links below. This fail is not in blocking policy yet

Test history | Ya make output | Test bloat

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
16876	16465	0	93	289	29

🟢 2025-08-22 16:14:10 UTC Build successful.