Add more logs to backup-related components

[Enjection]

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[Enjection]

Merge after #12267

[github-actions]

⚪ 2024-12-04 09:32:09 UTC Pre-commit check linux-x86_64-release-asan for 8bf3f4b has started.
⚪ 2024-12-04 09:32:56 UTC Artifacts will be uploaded here
⚪ 2024-12-04 09:36:38 UTC ya make is running...
🟡 2024-12-04 10:44:15 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?
13243	13166	0	24	7	46

🟢 2024-12-04 10:45:24 UTC Build successful.
🟢 2024-12-04 10:45:55 UTC ydbd size 4.9 GiB changed* by +62.7 KiB, which is < 100.0 KiB vs main: OK

ydbd size dash	main: 22abbae	merge: 8bf3f4b	diff	diff %
ydbd size	5 307 983 192 Bytes	5 308 047 416 Bytes	+62.7 KiB	+0.001%
ydbd stripped size	1 365 523 472 Bytes	1 365 538 704 Bytes	+14.9 KiB	+0.001%

^{*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]

⚪ 2024-12-04 09:33:13 UTC Pre-commit check linux-x86_64-relwithdebinfo for 8bf3f4b has started.
⚪ 2024-12-04 09:33:24 UTC Artifacts will be uploaded here
⚪ 2024-12-04 09:36:27 UTC ya make is running...
🟢 2024-12-04 10:30:05 UTC Tests successful.

Test history | Ya make output | Test bloat

TESTS	PASSED	ERRORS	FAILED	SKIPPED	MUTED?
20957	19447	0	0	1396	114

🟢 2024-12-04 10:31:48 UTC Build successful.
🟢 2024-12-04 10:32:05 UTC ydbd size 2.5 GiB changed* by +26.4 KiB, which is < 100.0 KiB vs main: OK

ydbd size dash	main: 22abbae	merge: 8bf3f4b	diff	diff %
ydbd size	2 701 651 016 Bytes	2 701 678 032 Bytes	+26.4 KiB	+0.001%
ydbd stripped size	483 580 528 Bytes	483 584 560 Bytes	+3.9 KiB	+0.001%

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