[codex] Fix code diagnostics LSP startup states

[ScriptedAlchemy]

Summary

• Capture LSP stderr during initialization so rust-analyzer startup failures show the real toolchain/proxy error instead of a generic crash.
• Mark language engines inactive when the indexed project does not need them, and skip inactive engines during refresh/backfill.
• Require adapter root markers for document selection where appropriate so stray files do not start irrelevant language servers.
• Update the Code Diagnostics dashboard to display the new inactive state.

Root Cause

The stdio LSP client discarded stderr and surfaced "closed before initialize response" when the rustup proxy exited early. The diagnostics broker then classified all refresh failures as crashed, so a missing or unavailable rust-analyzer binary appeared as a crash. Separately, dashboard document selection was extension-only, which could activate language servers for files that did not represent a real project for that adapter.

Impact

Rust analyzer failures now report the actionable rustup/toolchain stderr and are classified as unavailable instead of crashed. Language servers are only activated when project signals indicate they are needed, which reduces noisy startup attempts and makes Code Diagnostics state match the actual repository.

Validation

• cargo nextest run --test lsp_code_diagnostics_test --no-fail-fast
• cargo nextest run --test dashboard_code_diagnostics_api_test --no-fail-fast
• cargo nextest run documents_for_adapter --no-fail-fast
• cd dashboard && npm run test:node
• cd dashboard && npm run test:dom
• Live dashboard check confirmed Rust reports unavailable with captured rustup stderr, while unrelated languages report inactive.

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