Move connection drain from prepare to work

[lzydmxy]

Changelog category (leave one):

• Performance Improvement

Changelog entry (a user-readable short description of the changes that goes to CHANGELOG.md):

Move connection drain from prepare to work, and drain multiple connections in parallel.

Resolves #60844

[robot-clickhouse]

This is an automated comment for commit 582a427 with description of existing statuses. It's updated for the latest CI running

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Successful checks

Check name	Description	Status
A Sync	There's no description for the check yet, please add it to tests/ci/ci_config.py:CHECK_DESCRIPTIONS	✅ success
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
Fast test	Normally this is the first check that is ran for a PR. It builds ClickHouse and runs most of stateless functional tests, omitting some. If it fails, further checks are not started until it is fixed. Look at the report to see which tests fail, then reproduce the failure locally as described here	✅ success
Flaky tests	Checks if new added or modified tests are flaky by running them repeatedly, in parallel, with more randomization. Functional tests are run 100 times with address sanitizer, and additional randomization of thread scheduling. Integrational tests are run up to 10 times. If at least once a new test has failed, or was too long, this check will be red. We don't allow flaky tests, read the doc	✅ success
Install packages	Checks that the built packages are installable in a clear environment	✅ success
Mergeable Check	Checks if all other necessary checks are successful	✅ success
PR Check	There's no description for the check yet, please add it to tests/ci/ci_config.py:CHECK_DESCRIPTIONS	✅ 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
Style check	Runs a set of checks to keep the code style clean. If some of tests failed, see the related log from the report	✅ 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

Check name	Description	Status
AST fuzzer	Runs randomly generated queries to catch program errors. The build type is optionally given in parenthesis. If it fails, ask a maintainer for help	❌ failure
CI running	A meta-check that indicates the running CI. Normally, it's in success or pending state. The failed status indicates some problems with the PR	⏳ pending
Integration tests	The integration tests report. In parenthesis the package type is given, and in square brackets are the optional part/total tests	❌ failure
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	❌ failure