[BUG] Cowork "New Project" dialog shows mixed path separators on Windows

Bug

The "Create a new project" dialog in Cowork pre-fills the project location with a path that mixes \ and / separators on Windows:

C:\Users\<user>\Documents/Claude/Projects

The home portion (C:\Users\<user>\Documents) uses Windows-native backslashes, but the appended suffix (/Claude/Projects) uses forward slashes. This suggests the code is doing plain string concatenation like:

const defaultPath = os.homedir() + "/Documents/Claude/Projects";
// should be:
// path.join(app.getPath("documents"), "Claude", "Projects")

Why it matters

• Windows APIs accept both separators so functionality is not broken, but it looks unprofessional to users.
• Some downstream systems (WSL2 9P mount, third-party tools, log parsers) do not normalize gracefully and can produce edge-case failures.
• It leaks an implementation detail (hard-coded POSIX-style suffix) that suggests other path-handling code may share the same pattern.

Steps to reproduce

1. On Windows, open Claude Desktop → Cowork → Projects → "+" → "Start from scratch"
2. Observe the "Project location" field

Expected

All separators normalized to the platform native (\ on Windows):

C:\Users\<user>\Documents\Claude\Projects

Actual

C:\Users\<user>\Documents/Claude/Projects

Environment

• OS: Windows 10 (Korean UI)
• Claude Desktop: latest as of May 2026
• Cowork enabled

Fix suggestion

Replace the offending string concatenation with path.join() (Node) or the platform-appropriate equivalent. Likely a one-line change. Worth grepping the codebase for other "/"-suffixed path concatenations at the same time.