Remove usage of __async_repl attr from incr backup impl

[Enjection]

• draft
• fix naming
• fix ut
• fix attr

Changelog entry

...

Changelog category

• New feature
• Experimental feature
• Improvement
• Performance improvement
• User Interface
• Bugfix
• Backward incompatible change
• Documentation (changelog entry is not required)
• Not for changelog (changelog entry is not required)

Description for reviewers

...

[github-actions]

🟢 2025-09-08 12:51:24 UTC The validation of the Pull Request description is successful.

[github-actions]

⚪ 2025-09-08 12:51:46 UTC Pre-commit check linux-x86_64-release-asan for 068e410 has started.
⚪ 2025-09-08 12:52:00 UTC Artifacts will be uploaded here
⚪ 2025-09-08 12:55:56 UTC ya make is running...
🔴 2025-09-08 15:53:50 UTC Too many tests failed, NOT going to retry
🟡 2025-09-08 15:57:57 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?
17394	16414	0	547	399	34

🟢 2025-09-08 15:59:36 UTC Build successful.
🟡 2025-09-08 16:00:06 UTC ydbd size 4.0 GiB changed* by +120.9 KiB, which is >= 100.0 KiB vs main: Warning

ydbd size dash	main: 1222710	merge: 068e410	diff	diff %
ydbd size	4 295 853 480 Bytes	4 295 977 304 Bytes	+120.9 KiB	+0.003%
ydbd stripped size	1 489 104 504 Bytes	1 489 146 008 Bytes	+40.5 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]

⚪ 2025-09-08 12:51:54 UTC Pre-commit check linux-x86_64-relwithdebinfo for 068e410 has started.
⚪ 2025-09-08 12:52:10 UTC Artifacts will be uploaded here
⚪ 2025-09-08 12:56:09 UTC ya make is running...
🟡 2025-09-08 14:48:51 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?
40156	37386	0	6	2726	38

⚪ 2025-09-08 14:52:21 UTC ya make is running... (failed tests rerun, try 2)
🟡 2025-09-08 15:10:06 UTC Some tests failed, follow the links below. Going to retry failed tests...

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

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
549 (only retried tests)	518	0	1	3	27

⚪ 2025-09-08 15:10:17 UTC ya make is running... (failed tests rerun, try 3)
🟢 2025-09-08 15:24:22 UTC Tests successful.

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

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
277 (only retried tests)	253	0	0	0	24

🟢 2025-09-08 15:24:30 UTC Build successful.
🟢 2025-09-08 15:24:51 UTC ydbd size 2.3 GiB changed* by +77.6 KiB, which is < 100.0 KiB vs main: OK

ydbd size dash	main: 1222710	merge: 068e410	diff	diff %
ydbd size	2 444 286 464 Bytes	2 444 365 880 Bytes	+77.6 KiB	+0.003%
ydbd stripped size	511 671 432 Bytes	511 684 488 Bytes	+12.8 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}

[CyberROFL]

Тут пока не шипаю, но с изменениями в атрибутах согласен.

[github-actions]

⚪ 2025-09-08 18:24:51 UTC Pre-commit check linux-x86_64-relwithdebinfo for 3436a10 has started.
⚪ 2025-09-08 18:25:07 UTC Artifacts will be uploaded here
⚪ 2025-09-08 18:28:39 UTC ya make is running...
🟡 2025-09-08 20:28:43 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?
30900	29493	0	1	1369	37

⚪ 2025-09-08 20:31:25 UTC ya make is running... (failed tests rerun, try 2)
🟢 2025-09-08 20:43:30 UTC Tests successful.

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

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
405 (only retried tests)	381	0	0	1	23

🟢 2025-09-08 20:43:38 UTC Build successful.
🟢 2025-09-08 20:43:56 UTC ydbd size 2.3 GiB changed* by +86.0 KiB, which is < 100.0 KiB vs main: OK

ydbd size dash	main: d5fdf4b	merge: 3436a10	diff	diff %
ydbd size	2 444 278 240 Bytes	2 444 366 296 Bytes	+86.0 KiB	+0.004%
ydbd stripped size	511 670 408 Bytes	511 692 744 Bytes	+21.8 KiB	+0.004%

^{*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]

⚪ 2025-09-08 18:24:57 UTC Pre-commit check linux-x86_64-release-asan for 3436a10 has started.
⚪ 2025-09-08 18:25:12 UTC Artifacts will be uploaded here
⚪ 2025-09-08 18:28:32 UTC ya make is running...
🟡 2025-09-08 20:59:17 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?
15254	14827	0	123	277	27

🟢 2025-09-08 21:00:35 UTC Build successful.
🟡 2025-09-08 21:00:59 UTC ydbd size 4.0 GiB changed* by +115.2 KiB, which is >= 100.0 KiB vs main: Warning

ydbd size dash	main: d5fdf4b	merge: 3436a10	diff	diff %
ydbd size	4 295 846 432 Bytes	4 295 964 424 Bytes	+115.2 KiB	+0.003%
ydbd stripped size	1 489 102 872 Bytes	1 489 140 920 Bytes	+37.2 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}