rc-bridge: Fix developer UI sentinel page

[ydbot]

Cherry-pick:

• PR Fix developer UI sentinel page #23612

PR was created by cherry-pick workflow run

[github-actions]

⚪ 2025-09-04 09:48:34 UTC Pre-commit check linux-x86_64-relwithdebinfo for c798082 has started.
⚪ 2025-09-04 09:48:54 UTC Artifacts will be uploaded here
⚪ 2025-09-04 09:52:46 UTC ya make is running...
🟡 2025-09-04 11:03:21 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?
29826	28422	0	2	1367	35

⚪ 2025-09-04 11:05:55 UTC ya make is running... (failed tests rerun, try 2)
🟢 2025-09-04 11:20:46 UTC Tests successful.

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

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
436 (only retried tests)	410	0	0	1	25

🟢 2025-09-04 11:21:01 UTC Build successful.

[github-actions]

⚪ 2025-09-04 09:49:16 UTC Pre-commit check linux-x86_64-release-asan for c798082 has started.
⚪ 2025-09-04 09:49:30 UTC Artifacts will be uploaded here
⚪ 2025-09-04 09:52:42 UTC ya make is running...
🟡 2025-09-04 11:39:41 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?
14512	14103	0	100	283	26

🟢 2025-09-04 11:41:02 UTC Build successful.