fix(doctor): address Sage review findings on duplication-check PR #601

[HenryLach]

Follow-up to PR #601. Sage's review flagged three minor issues; all three are addressed here.

Findings addressed

1. Summary message no longer recommends taskplane init for duplicate installs ([minor], confidence high)

Sage's finding: the duplication block increments issues, so doctor exits non-zero and the final line was '$N issue(s) found. Run taskplane init to fix config issues.' — actively misleading when the underlying issue is a duplicate install (whose fix is npm uninstall -g taskplane, not init).

Fix: track a separate duplicationDetected flag; emit a context-aware summary:

• with duplication: 'See remediation hints above (npm uninstall -g taskplane for the duplicate install)'
• without: 'See remediation hints above; run taskplane init to fix config issues'

Either way the FAIL exit code is preserved so CI gates on doctor still catch the issue.

2. PowerShell-aware remediation in the duplication block ([minor], confidence high)

Sage's finding: the inline fix only showed bash syntax (export PATH=...), even though Taskplane is cross-platform and the duplicate-install issue is especially common on Windows + NVM-for-Windows (see #598). Windows users would copy/paste a non-working command.

Fix: branches on process.platform:

• Windows: shows the $env:PATH = '$HOME\.pi\...' PowerShell snippet first with the Git Bash equivalent as a secondary 'or, for Git Bash:' line
• Non-Windows: shows the bash form as before

3. 5-second timeout on execSync('npm root -g') ([question], medium confidence — verify)

Sage's finding: execSync had no timeout, raising potential hang risk if npm is slow or misconfigured.

Fix: added timeout: 5000 to the execSync options. On timeout the catch branch runs, returning null and silently skipping the duplication check (best-effort by design).

Findings deliberately NOT addressed

Sage's centralization suggestion (part of finding 3)

Sage suggested centralizing npm-root probing by sharing logic with extensions/taskplane/path-resolver.ts. I'm not doing this, with reasoning:

• bin/taskplane.mjs is a self-contained CLI script with no cross-module imports from the extensions tree
• Pulling in the resolver would expand the import surface for what amounts to a 5-line execSync call
• The two functions have distinct purposes: the path resolver finds Pi/Taskplane for spawning; this helper detects on-disk duplication for diagnostics
• Sage flagged this as 'medium confidence — verify'; on verification, the local copy is the right call

Out-of-scope: docs/specifications/** references to npm install -g taskplane

Sage correctly labeled this as out-of-scope. Leaving it for a future docs consistency sweep.

Validation

Gate	Result
npm run typecheck	✅ pass
npm run format:check	✅ pass
Full test suite	✅ 3,714 / 3,715 pass, 1 skipped — zero new failures
Doctor smoke (no duplication)	✅ clean output, summary unchanged
Doctor smoke (simulated dup, Windows)	✅ WARN block fires, PowerShell line first, Git Bash secondary, FAIL summary references npm uninstall instead of taskplane init

Diff summary

Single file: bin/taskplane.mjs, +42 −6.