feat(prompt): compose explicit backend sections

[owainlewis]

Summary

Compose conversation and job requests through one component with explicit Push policy, user identity, resolved path, and fresh context sections. JSON framing keeps identity, message metadata, current content, and bounded history inside their owned sections while Claude Code, Codex, and Pi retain their native system-prompt mechanisms. Fresh, resumed, and rebuilt sessions now share the same context schema.

Why

The previous path, identity, policy, and rehydration strings were assembled separately, which made ownership and precedence harder to verify. This gives all three adapters one documented semantic boundary without adding a generic instruction handbook or changing ordinary reply delivery.

Test plan

• cargo fmt --all -- --check
• cargo clippy --locked --all-targets -- -D warnings
• cargo build --locked
• cargo test --locked (349 unit, 1 docs, 12 init CLI, and 3 manual crash tests passed)
• GitHub CI run #251 passed on Ubuntu, macOS, and docs
• Fresh subagent review approved after both findings were addressed
• No PR comments or review threads were present after CI completed

Risks

Prompt text changes for every conversation and job. Unit, gateway, job, and adapter contract tests cover the boundary, but live invocation against installed Claude Code, Codex, and Pi binaries was not performed.

Related issue

Closes #167