fix(api): stabilize Fly deploy startup

[ComputelessComputer]

Summary:

• Stage Infisical /ai secrets into Fly before bluegreen API deploys.
• Stop eagerly opening the unused support Postgres pool during API startup.
• Raise the STT proxy request body limit so long batch audio uploads reach provider routing.

Verification:

• pnpm exec dprint fmt crates/transcribe-proxy/src/routes/mod.rs
• cargo check -p api
• API CD workflow passed: https://github.com/fastrepl/anarlog/actions/runs/26267517625
• https://api.char.com/health returns 0.0.48
• https://api.anarlog.so/health returns 0.0.48
• Soniox direct/proxy STT e2e checks passed on PR fix(api): stabilize Fly deploy startup #5298

[netlify]

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