perf: avoid forced warm-start compiles

[sophiathedev]

Summary

• choose the startup compile mode from the persisted search index status
• separate first-compile dependency preparation from the Mix --force option
• preserve forced compilation after an engine-node crash deletes build artifacts
• cover cold, warm, forwarded-mode, and repeated-build behavior

Testing

• mix test --warnings-as-errors (engine: 1,162 passed; expert: 844 passed)
• mix compile --warnings-as-errors
• mix format --check-formatted
• mix credo
• mix dialyzer --force-check

Closes #863