Fix GUI subprocess PATH

[jimmystridh]

Fixes GUI-launched Git/GitHub commands missing user PATH.

SlayZone was spawning Git worktree operations directly from Electron PATH and running gh through interactive zsh. That broke Git LFS hooks when Homebrew was missing from PATH, and let zsh prompt/gitstatus noise make gh PR listing fail.

This moves enriched PATH into the shared platform shell helper, applies it to worktree subprocesses and setup scripts, and runs gh directly with that environment so shell startup files cannot contaminate stderr.

Validation:

• @slayzone/platform tests
• @slayzone/worktrees typecheck
• @slayzone/terminal typecheck
• @slayzone/app typecheck
• stripped-PATH smoke for git-lfs and gh pr list
• macOS arm64 app build + codesign verify

Greptile Summary

This PR fixes GUI-launched subprocess PATH handling for Git and GitHub CLI workflows. The main changes are:

• Adds marker-based PATH probing for noisy shell startup output.
• Applies the enriched PATH to worktree subprocess execution.
• Runs gh directly through the resolved binary path instead of through the interactive shell.
• Uses platform-specific path helpers for CLI install paths.
• Skips an unwritable-directory migration test on Windows.

Confidence Score: 5/5

This looks safe to merge.

• No blocking issues found in the changed code.

Important Files Changed

Filename	Overview
packages/domains/terminal/src/main/shell-env.ts	Adds marker-filtered PATH extraction and resolves binaries using enriched environment state.
packages/domains/worktrees/src/main/exec-async.ts	Injects the enriched PATH into worktree subprocesses.
packages/domains/worktrees/src/main/gh-cli.ts	Runs the resolved gh binary directly to avoid shell startup output corrupting command results.
packages/shared/platform/src/cli-install.ts	Uses platform-specific path joins for CLI install target and Windows shim copy paths.

_{Reviews (1): Last reviewed commit: "fix(platform): pass Windows platform tes..." | Re-trigger Greptile}

Context used:

• Context used - CLAUDE.md (source)
• Context used - AGENTS.md (source)