Backport #70530 to 24.9: Make async insert print nothing

[robot-ch-test-poll4]

Original pull-request #70530
Cherry-pick pull-request #70576

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-poll2]

This is an automated comment for commit e224e3e with description of existing statuses. It's updated for the latest CI running

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Successful checks

Check name	Description	Status
Builds	There's no description for the check yet, please add it to tests/ci/ci_config.py:CHECK_DESCRIPTIONS	✅ 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
Install packages	Checks that the built packages are installable in a clear environment	✅ success
Integration tests	The integration tests report. In parenthesis the package type is given, and 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
Stateless tests	Runs stateless functional tests for ClickHouse binaries built in various configurations -- release, debug, with sanitizers, etc	✅ success
Stress test	Runs stateless functional tests concurrently from several clients to detect concurrency-related errors	✅ success