[BUG] Windows: `claude auth login` / OAuth browser doesn't open automatically in Git Bash — no fallback to cmd.exe /c start (regression since 2.1.141)

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

On Windows, `claude auth login` (and any other OAuth flow driven by the CLI, e.g. `/mcp` authentication) does not open the default browser automatically when running from a Git Bash (MSYS2/MINGW64) shell. The command prints the login URL and device code, and the user has to copy-paste them by hand.

This used to work — the browser opened automatically in earlier versions. It broke as a regression starting with v2.1.141 (auto-update, 2026-05-14): the browser-open logic changed and, in a Git Bash session where `BROWSER` and `DISPLAY` are unset, there is no fallback to `cmd.exe /c start` anymore. The equivalent issue for MCP auth in the same environment (#59194) documents the same regression and root cause, but was auto-closed as stale/"not planned" without a fix; the underlying `claude auth login` case (not just MCP) is still broken.

### What Should Happen?

On Windows, when `BROWSER` is unset and there's no `DISPLAY` (i.e. a normal Git Bash session, not X11), the CLI should fall back to `cmd.exe /c start "" ` (or an equivalent native Windows browser-open call), the same way it apparently did before v2.1.141, instead of silently doing nothing and leaving the user to copy-paste the URL by hand.

### Error Messages/Logs

```shell
No error is printed — the CLI prints the OAuth URL and device code as normal and waits for the code, it just never spawns a browser process. Confirmed via Task Manager: no new browser process appears after running `claude auth login`.
```

### Steps to Reproduce

1. On Windows, open Git Bash (MINGW64) — the default shell bundled with Git for Windows.
2. Do not set a `BROWSER` environment variable.
3. Run `claude auth login`.
4. Expected: the default browser (Chrome, correctly registered as the Windows default handler for http/https on this machine) opens automatically to the OAuth URL.
5. Actual: nothing opens. The CLI prints the URL and code and waits; the user has to copy the URL into a browser by hand and then copy the resulting code back into the terminal.
6. Workaround that restores the old behavior: add `{ "env": { "BROWSER": "cmd.exe /c start \"\"" } }` to `~/.claude/settings.json`, as documented in the comments on #59194. This should not be necessary — it worked with zero configuration before v2.1.141.

### Claude Model

None

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

2.1.139

### Claude Code Version

2.1.237 (Claude Code)

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

Other

### Additional Information

This is the `claude auth login` / general OAuth-CLI-flow instance of the exact regression described in #59194 ("OAuth browser does not open for HTTP MCP servers on Windows"), which was auto-closed as stale/"not planned" in June without a fix. Filing separately since #59194 is closed and the underlying regression (no `cmd.exe` fallback since 2.1.141 in a Git-Bash/no-DISPLAY environment) is still present for at least the `claude auth login` flow, not just MCP auth. Also closed/related: #44350 (dup), #30902 (dup).

Workaround for anyone hitting this in the meantime: `~/.claude/settings.json` → `{ "env": { "BROWSER": "cmd.exe /c start \"\"" } }` (the empty quotes after `start` are required — that's the window-title argument `start` expects). Would be good if this became the default behavior on Windows again rather than something every affected user has to independently discover and configure by hand.

Start by reproducing `claude auth login` in Windows Git Bash with `BROWSER` and `DISPLAY` unset, then trace the CLI's OAuth browser-opening path and its Windows handling. Done means the default browser opens automatically through a native Windows fallback, while the existing login URL and code flow still work.

索引モデルが issue の本文から書いたものです。