[fix][client] Make ClientBuilder serializable (#25730)

[jiangpengcheng]

Motivation

cherry-pick #25730 to branch-4.0

Modifications

Verifying this change

• Make sure that the change passes the CI checks.

(Please pick either of the following options)

This change is a trivial rework / code cleanup without any test coverage.

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This change is already covered by existing tests, such as (please describe tests).

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This change added tests and can be verified as follows:

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• Added integration tests for end-to-end deployment with large payloads (10MB)
• Extended integration test for recovery after broker failure

Does this pull request potentially affect one of the following parts:

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• Dependencies (add or upgrade a dependency)
• The public API
• The schema
• The default values of configurations
• The threading model
• The binary protocol
• The REST endpoints
• The admin CLI options
• The metrics
• Anything that affects deployment