fix: resolve dependencies via registry Machine/User PATH on Windows(#504)

[EnmaJim]

Linked issue

Closes #658

Summary of changes

On Windows, dotbot reported git: MISSING / claude: MISSING and the workflow child window flashed and died whenever the process inherited a PATH missing the Machine or User registry scope (e.g. Git installed system-wide, Claude installed per-user) — even though both tools worked in the user's terminal. Every detection site used Get-Command, which only searches the process PATH.

Fix:

• New in Dotbot.Core (dependency-free, imported first by every entry point):
  • Resolve-DotbotExternalCommand — resolves a command via the process PATH, falling back to a registry Machine → User PATH scan on Windows; reports which scope the tool was found in and can repair the session PATH.
  • Repair-DotbotProcessPath — one-time, append-only merge of registry PATH directories missing from $env:PATH; opt-out via DOTBOT_SKIP_PATH_REPAIR; no-op on non-Windows.
• Test-Preflight and the Test-GitReadyForWorktree git gate resolve through the new resolver with session repair. Registry-scope hits produce an actionable check line naming the tool, the PATH scope, the directory, and the permanent fix. The exact MISSING strings are unchanged for truly-absent tools.
• The three entry-point preambles (bin/dotbot.ps1, Invoke-DotbotProcess.ps1, src/ui/server.ps1) call Repair-DotbotProcessPath once, transparently healing all downstream spawn sites (harness adapters, ProcessStream) and UI capability probes without modifying them.
• dotbot doctor detects the split instead of healing it (the CLI preamble deliberately skips repair for doctor so it observes the raw inherited PATH): a registry-only hit emits a split PATH detected Warn plus session and permanent fix commands.
• Secondary bug fixed: bin/dotbot.ps1 swallowed doctor.ps1's exit code — dotbot doctor exited 0 even with failing checks. The dispatcher now propagates it (same pattern as dotbot run).

Testing notes

tests/Test-DependencyPathResolution.ps1 encodes the issue's acceptance criteria and was failing 11/18 before the fix — it now passes 18/18. It simulates the split by spawning child pwsh processes with tool directories stripped from the process PATH while the registry PATH stays intact, and covers: preflight resolution via Machine and User scopes, the actionable scope-naming messages, doctor's split detection, and doctor exit-code propagation (with two scenarios that stay non-zero even after the PATH fix, so the propagation assertion can't trivially pass).

• pwsh -NoProfile -ExecutionPolicy Bypass -File tests/Test-DependencyPathResolution.ps1 → 18 passed, 0 failed.
• pwsh tests/Run-Tests.ps1 -Layer all → Layers 1–3 all passed (including the static scanners and both Layer-3 mock-provider suites; the append-only repair preserves mock-first PATH ordering).
• Live verification on a real split-PATH machine (git in Machine PATH, claude in User PATH): preflight passes from stripped shells naming the correct scope; post-preflight Get-Command succeeds in the same process (session-repair proof); a directory freshly added to the real User PATH is picked up; removing the tool everywhere still yields the exact MISSING failure; end-to-end dotbot run smoke-test from a claude-stripped shell survives preflight and runs, while dotbot doctor from the same shell reports the split and exits 1.

Checklist

• Tests added or updated
• Docs updated (if behaviour changed)
• Linked issue exists
• Follows the contribution guide

[carlospedreira]

Reviewed the rebased final head. PATH repair opt-out, split-PATH doctor behavior, deterministic scope/elevation coverage, executable precedence, and cross-platform behavior are addressed; local Layers 1-3 and all required CI checks pass.