fix(logging): preserve transport and worker log context

[debugmcpdev]

Description

Fixes #533 and #534.

• attaches the shared file transport to the deprecated SSE command's CLI logger before its first lifecycle message, matching HTTP behavior
• maps worker stderr prefixes (DEBUG, INFO, WARN/WARNING, and ERROR) to the corresponding server logger level
• keeps indented and structural continuation lines with the preceding diagnostic while leaving fresh unprefixed output at error level
• prefixes bootstrap and worker-entry lifecycle diagnostics so normal startup output is not reported as an error
• preserves the bounded, sanitized captured stderr buffer byte-for-line as before

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• Test improvement

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented hard-to-understand classification behavior
• My changes generate no new warnings
• I have added tests that prove the fixes are effective
• New and existing unit tests pass locally with my changes
• No downstream publication is required

Testing

pnpm run build
pnpm run test:unit                    # 230 files, 4,273 tests
pnpm run test:integration             # 8 passed / 2 skipped; 23 passed / 5 skipped
pnpm run lint
pnpm run check:personal-paths
git diff --check

Dogfooding through the source dev proxy also covered both transports:

• SSE lifecycle/deprecation output appeared in the requested --log-file
• a real JavaScript debug flow (breakpoint, locals, evaluation, continue, output, close) produced 294 worker-stderr records with no normal startup/debug record promoted to error

Test configuration: Windows x64, Node.js 24.14.1, pnpm 10.33.0

Related Issues

• Closes sse: --log-file never reaches the CLI logger, so sse-command lines (incl. stale-session reap warnings) are invisible #533
• Closes Worker stderr is forwarded into the server log at error level, drowning real errors in [DEBUG] diagnostics #534

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Reviewer: @debugmcp

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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