refactor(lsp): unify command detection

[beruro]

Problem

The LSP crate had three independent implementations for checking whether a command exists. One explicitly forwarded the app-adjusted PATH while the lint and workspace-scan copies did not, so installed-tool results could differ by surface and future platform fixes had to be repeated.

Solution

Introduce one crate-owned command detection helper and route LSP discovery, package-manager selection, install preflight, lint-tool detection, and both workspace scan paths through it. The helper explicitly forwards the current PATH, preserves Windows console suppression, and keeps the existing public commands::discovery::command_exists entry point as a re-export for compatibility. Regression tests cover a known platform shell and a guaranteed-missing command.

Potential risks

Tool availability now consistently uses the explicit-PATH behavior that discovery already used. This could make a previously inconsistent lint surface recognize a tool added to the app process PATH, which is the intended convergence. Command execution count and timing remain unchanged; no cache was added, avoiding stale results after PATH changes. Rollback is a single-commit revert.

Architecture and performance

• Covered ownership, public API compatibility, platform behavior, dependency direction, scan/install consumers, and test boundaries.
• Intentionally skipped wire types, persistence, FSM, UI/rendering, and initialization parity because they are unchanged.
• Performance verdict: pass/neutral. Foreground and orchestrated scans make the same number of lookup processes as before; no polling, retry loop, timer, subscription, cache, or retained state was added.
• Lifecycle matrix: active scan behavior is unchanged; idle, hidden, closed, and repeated-open states retain no command-detection resources.

Verification

• cargo fmt --all -- --check — passed after formatting.
• cargo test -p lsp --lib — 112 passed.
• cargo clippy -p lsp --all-targets --no-deps -- -D warnings — passed.
• Repository commit hook — scoped LSP Cargo clippy passed.
• git diff --check — passed.
• No TypeScript or UI files changed, so frontend typecheck and visual evidence are not applicable.

[beruro]

Superseded by #780, which preserves this change as an independent commit and has passed the consolidated CI suite. The source branch is retained for recovery.