Fix PowerShell PATH refresh and integration upgrades

[CheckPickerUpper]

Summary

• refresh the current PowerShell process PATH even when the install directory is already in persisted user PATH
• normalize PATH comparisons to avoid duplicate entries across Windows path spellings
• replace existing managed profile blocks so legacy bare-rep integrations migrate to the guarded resolver
• retain an actionable recovery function when the binary is genuinely unavailable

Closes #5

Verification

• cargo test --all-targets
• static installer assertions

Note: a Windows PowerShell fresh-session run is still required for full platform-specific verification; this Linux workspace has no PowerShell runtime.

[github-actions]

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