Move balancer to batch pool (#11420)

[robdrynkin]

• Not for changelog (changelog entry is not required)

[github-actions]

⚪ 2025-01-08 16:08:28 UTC Pre-commit check for 1308a9e has started.
⚪ 2025-01-08 16:11:06 UTC Build linux-x86_64-release-asan is running...
🟢 2025-01-08 16:34:37 UTC Build successful.
⚪ 2025-01-08 16:34:55 UTC Tests are running...
🔴 2025-01-08 18:41:30 UTC Some tests failed, follow the links below.

Test history | Test log

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
10578	10474	0	27	29	48

🟢 2025-01-08 18:42:23 UTC ydbd size 5.6 GiB changed* by +352 Bytes, which is < 100.0 KiB vs stream-nb-24-3: OK

ydbd size dash	stream-nb-24-3: 0927051	merge: 1308a9e	diff	diff %
ydbd size	6 007 227 752 Bytes	6 007 228 104 Bytes	+352 Bytes	+0.000%
ydbd stripped size	1 504 813 248 Bytes	1 504 813 312 Bytes	+64 Bytes	+0.000%

^{*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]

⚪ 2025-01-08 16:08:48 UTC Pre-commit check for 1308a9e has started.
⚪ 2025-01-08 16:11:25 UTC Build linux-x86_64-relwithdebinfo is running...
🟢 2025-01-08 16:52:39 UTC Build successful.
⚪ 2025-01-08 16:53:04 UTC Tests are running...
🔴 2025-01-08 18:35:16 UTC Some tests failed, follow the links below.

Test history | Test log

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
14902	13547	0	11	1301	43

🟢 2025-01-08 18:36:05 UTC ydbd size 8.3 GiB changed* by +960 Bytes, which is < 100.0 KiB vs stream-nb-24-3: OK

ydbd size dash	stream-nb-24-3: 0927051	merge: 1308a9e	diff	diff %
ydbd size	8 875 724 152 Bytes	8 875 725 112 Bytes	+960 Bytes	+0.000%
ydbd stripped size	483 994 632 Bytes	483 994 824 Bytes	+192 Bytes	+0.000%

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