Backport #61869 to 24.3: Fix flaky tests 2 (stateless, integration)

[robot-ch-test-poll2]

Original pull-request #61869
Cherry-pick pull-request #62029

This pull-request is a last step of an automated backporting.
Treat it as a standard pull-request: look at the checks and resolve conflicts.
Merge it only if you intend to backport changes to the target branch, otherwise just close it.

[robot-ch-test-poll3]

This is an automated comment for commit 969cc4e with description of existing statuses. It's updated for the latest CI running

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Successful checks

Check name	Description	Status
ClickBench	Runs [ClickBench](https://github.com/ClickHouse/ClickBench/) with instant-attach table	✅ success
ClickHouse build check	Builds ClickHouse in various configurations for use in further steps. You have to fix the builds that fail. Build logs often has enough information to fix the error, but you might have to reproduce the failure locally. The cmake options can be found in the build log, grepping for cmake. Use these options and follow the general build process	✅ success
Compatibility check	Checks that clickhouse binary runs on distributions with old libc versions. If it fails, ask a maintainer for help	✅ success
Docker keeper image	The check to build and optionally push the mentioned image to docker hub	✅ success
Docker server image	The check to build and optionally push the mentioned image to docker hub	✅ success
Docs check	Builds and tests the documentation	✅ success
Install packages	Checks that the built packages are installable in a clear environment	✅ success
Performance Comparison	Measure changes in query performance. The performance test report is described in detail here. In square brackets are the optional part/total tests	✅ success
Stateful tests	Runs stateful functional tests for ClickHouse binaries built in various configurations -- release, debug, with sanitizers, etc	✅ success
Unit tests	Runs the unit tests for different release types	✅ success
Upgrade check	Runs stress tests on server version from last release and then tries to upgrade it to the version from the PR. It checks if the new server can successfully startup without any errors, crashes or sanitizer asserts	✅ success