feat: add coding-agent sidecar integrations

[willkill07]

Overview

Adds a Rust nemo-flow-sidecar binary for coding-agent observability plus installable hook integrations and setup documentation for Claude Code, Codex, and Cursor. The sidecar accepts canonical agent hook payloads, normalizes them internally, and provides passthrough OpenAI/Anthropic gateway routes for LLM lifecycle observability.

• I confirm this contribution is my own work, or I have the right to submit it under this project's license.
• I searched existing issues and open pull requests, and this does not duplicate existing work.

Details

• Adds the nemo-flow-sidecar crate with /hooks/claude-code, /hooks/codex, and /hooks/cursor endpoints.
• Adds passthrough gateway routes for OpenAI Responses, OpenAI Chat Completions, Anthropic Messages, Anthropic token counting, and model listing.
• Adds sidecar session management for agent, subagent, tool, LLM, ATIF, and OpenInference lifecycle handling.
• Adds nemo-flow-sidecar install claude-code|codex|cursor and hook-forward support with safe merge, backup, --dry-run, --print, metadata, ATIF, OpenInference, plugin config, and gateway mode options.
• Adds installable Claude Code and Codex hook/plugin bundles plus a Cursor hook bundle under integrations/coding-agents/.
• Adds end-to-end sidecar docs and self-contained per-agent README setup guides.
• Updates Rust attribution data for the new sidecar dependencies.

Validation run locally:

• cargo test -p nemo-flow-sidecar
• just test-rust
• just docs
• cargo clippy -p nemo-flow-sidecar --all-targets -- -D warnings
• Commit pre-checks passed with lychee skipped because it failed on unrelated generated Rust API doc links in docs/reference/api/rust/_generated/....

Where should the reviewer start?

Start with crates/sidecar/src/server.rs for the external HTTP surface, then crates/sidecar/src/installer.rs for the install/merge behavior, and integrations/coding-agents/README.md for the packaged integration contract.

Related Issues: (use one of the action keywords Closes / Fixes / Resolves / Relates to)

• Closes NMF-57
• Closes NMF-58
• Closes NMF-59
• Closes NMF-60

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