RUST-1842 Update prose tests for mongos deprioritization during retryable ops#1397

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JamieTsai1024 wants to merge 6 commits intomongodb:mainfrom

JamieTsai1024:RUST-1842

Commits on Jun 12, 2025

Commits on Jun 13, 2025

Temporary logs to verify code paths
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Commits on Jun 16, 2025

Log considered servers for selection
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Commits on Jun 17, 2025

Replace close connection for different_mongos tests
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Remove close_connection for failpoints on different mongos retryable tests
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