Fix run JSON auth output contamination

[OnlyYu1996]

Summary

• send non-TUI tracing logs to stderr instead of stdout
• keep cortex run --format json stdout parseable when auth setup emits warnings
• fix a stale test import so cortex-cli tests compile on current main

Fixes PlatformNetwork/bounty-challenge#53157

Verification

• cargo fmt --package cortex-cli --check
• cargo check --package cortex-cli --lib
• cargo test --package cortex-cli cli::args::tests::test_log_level_as_filter_str -- --nocapture
• git diff --check
• cargo build --package cortex-cli --bin Cortex
• clean-home target/debug/Cortex run --format json hello with stdout parsed by jq, no auth WARN in stdout, and auth WARN present on stderr

[greptile-apps]

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