[Bug] Path Resolution Fails on Windows with Case-Sensitive Path Matching

Bug Description
Warning in windows IDE environment about "native installatione xists but is not in your path" when the file path uses case insensitive path string while actual path folders contain capitalizations. (example: path is set to c:\Users\admin\.local\bin, claude code expects capital c C:\User\admin\,local\bin. Been identified in 1.0.86, 88, 110, and 112 versions

Environment Info

• Platform: win32
• Terminal: null
• Version: 1.0.112
• Feedback ID: ebe1ff80-07c7-4ab3-97dc-b3bc1211d32a

Errors

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![Image](https://github.com/user-attachments/assets/9c712cf0-9f16-4ad1-9309-c781cffc2e54)

<img width="1222" height="953" alt="Image" src="https://github.com/user-attachments/assets/b320768b-697d-43c8-925e-0dd6d3ad325e" />