fix(backend): prefer path root for bin path if it contains an executable

[risu729]

#7138 broke e2e-win/7z.Tests.ps1.

7z2500-extra.7z has a directory structure like:

7z2500-extra$ ls -R
.:
7za.dll  7za.exe  7zxa.dll  Far  License.txt  arm64  history.txt  readme.txt  x64

./Far:
7-ZipEng.hlf  7-ZipEng.lng  7-ZipFar.dll  7-ZipFar64.dll  7-ZipRus.hlf  7-ZipRus.lng  7zToFar.ini  far7z.reg  far7z.txt

./arm64:
7-ZipFar.dll  7za.dll  7za.exe  7zxa.dll

./x64:
7za.dll  7za.exe  7zxa.dll

So if both /arm64 and /x64 are on PATH, /arm64/7za.exe is used even on x64 arch.

This PR fixes this by prioritising the root path if the root path contains an executable file.

---

Note

Bin path discovery now uses the install root if it contains an executable and recognizes executable-only subdirs; docs updated and e2e adjusted.

• Backend (GitHub/GitLab unified)
  • src/backend/github.rs bin path discovery:
    • Prefer install root when it contains any executable file.
    • If a subdirectory contains executables directly, treat that subdirectory as a bin path.
• Docs
  • Update binary path lookup order in docs/dev-tools/backends/github.md and docs/dev-tools/backends/gitlab.md to reflect new root/subdir executable handling.
• Tests
  • e2e/backend/test_github: add mise uninstall before installs for clean runs.
• Lockfile
  • Refresh mise.lock with added size/checksum metadata and removed unused entries.

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[Copilot]

Pull request overview

This PR improves the binary path discovery logic for GitHub and GitLab backends by prioritizing the root install path when it contains executable files, preventing unnecessary deep directory searches.

Key changes:

• Added a new check in discover_bin_paths() to detect executables in the root install directory before searching subdirectories
• Updated documentation for both GitHub and GitLab backends to reflect the new 6-step binary path lookup order

Reviewed changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 2 comments.

File	Description
src/backend/github.rs	Adds logic to check for executables in the root install path (step 3 in the lookup order), positioned between checking for bin/ directory and searching subdirectories
docs/dev-tools/backends/github.md	Updates binary path lookup documentation to include the new step 3 and renumbers subsequent steps
docs/dev-tools/backends/gitlab.md	Updates binary path lookup documentation consistently with GitHub backend changes

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[jdx]

bugbot run

[cursor]

✅ Bugbot reviewed your changes and found no bugs!

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