chore(web): Add debug logging to measure homepage load performance

[brendan-kellam]

We were getting reports of poor homepage load performance. This adds some server-side debug logging to the homepage that attempts to measure where the performance bottleneck is.

Debug logging can be enabled by setting SOURCEBOT_LOG_LEVEL="debug"

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✨ Finishing touches

🧪 Generate unit tests

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch bkellam/instrument_homepage

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[github-actions]

@brendan-kellam your pull request is missing a changelog!