Integrate tracing into Bridged proxy, add BridgedRequest span

[serbel324]

Changelog entry

Support Distributed Storage tracing in configuration with multiple piles

Changelog category

• Improvement

[github-actions]

🟢 2025-08-22 07:01:19 UTC The validation of the Pull Request description is successful.

[github-actions]

⚪ 2025-08-22 07:04:25 UTC Pre-commit check linux-x86_64-relwithdebinfo for b9edd6b has started.
⚪ 2025-08-22 07:04:39 UTC Artifacts will be uploaded here
⚪ 2025-08-22 07:08:19 UTC ya make is running...
🟡 2025-08-22 09:05:30 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?
39527	36769	0	5	2714	39

⚪ 2025-08-22 09:08:58 UTC ya make is running... (failed tests rerun, try 2)
🟢 2025-08-22 09:23:19 UTC Tests successful.

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

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
610 (only retried tests)	584	0	0	1	25

🟢 2025-08-22 09:23:28 UTC Build successful.
🟢 2025-08-22 09:23:50 UTC ydbd size 2.3 GiB changed* by +98.3 KiB, which is < 100.0 KiB vs main: OK

ydbd size dash	main: 671ffc8	merge: b9edd6b	diff	diff %
ydbd size	2 429 279 360 Bytes	2 429 380 032 Bytes	+98.3 KiB	+0.004%
ydbd stripped size	509 285 608 Bytes	509 302 888 Bytes	+16.9 KiB	+0.003%

^{*please be aware that the difference is based on comparing your commit and the last completed build from the post-commit, check comparation}

[github-actions]

⚪ 2025-08-22 07:05:49 UTC Pre-commit check linux-x86_64-release-asan for b9edd6b has started.
⚪ 2025-08-22 07:05:53 UTC Artifacts will be uploaded here
⚪ 2025-08-22 07:09:37 UTC ya make is running...
🟡 2025-08-22 09:44:08 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?
16898	16415	0	115	338	30

🟢 2025-08-22 09:45:41 UTC Build successful.
🟡 2025-08-22 09:46:10 UTC ydbd size 4.0 GiB changed* by +174.4 KiB, which is >= 100.0 KiB vs main: Warning

ydbd size dash	main: 671ffc8	merge: b9edd6b	diff	diff %
ydbd size	4 268 990 032 Bytes	4 269 168 608 Bytes	+174.4 KiB	+0.004%
ydbd stripped size	1 481 448 056 Bytes	1 481 492 120 Bytes	+43.0 KiB	+0.003%

^{*please be aware that the difference is based on comparing your commit and the last completed build from the post-commit, check comparation}