Native Windows section of README/docs still describes pre-v0.37.0 CLAUDE.md fallback

The Native Windows section of README.md and matching docs still describe the pre-v0.37.0 fallback behavior, where rtk init -g on native Windows could not install a working hook and fell back to CLAUDE.md injection. Since v0.37.0 (CHANGELOG: hooks: windows use 'rtk hook claude' no fallback), rtk init -g installs the native rtk hook claude PreToolUse hook on all platforms including Windows, and the rtk-rewrite.sh shell script is no longer required for Claude Code.

Stale claims I noticed while reading the docs from a Windows install:

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/README.md#L90

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/README.md#L317

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/README.md#L330-L350

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/docs/guide/resources/troubleshooting.md#L119

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/docs/guide/getting-started/supported-agents.md#L182

Each one tells Windows users the auto-rewrite hook does not work and that rtk init -g falls back to CLAUDE.md injection.

Looking at the current code, rtk init -g for Claude Code writes a Bash matcher with "command": "rtk hook claude" into ~/.claude/settings.json unconditionally, on Windows the same as macOS/Linux — no cfg!(target_os = \"windows\") branch and no shell-script dependency:

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/src/hooks/constants.rs#L12

https://github.com/rtk-ai/rtk/blob/39583cf22b0a73ef78f935d8ada1c87a9a10e852/src/hooks/init.rs#L1054-L1086

I can confirm from a native Windows install (v0.42.0, Claude Code) that the hook is in settings.json as rtk hook claude and rewrites Bash tool calls transparently — no CLAUDE.md injection involved.

One related caveat that might be worth mentioning in the same place: the hook matcher is hardcoded to Bash, so when Claude Code is configured to use the PowerShell tool (CLAUDE_CODE_USE_POWERSHELL_TOOL=1), commands are not rewritten. That gap is already tracked in #1319, but readers landing on the Windows section today may not realize the Bash-tool-only scope is the only real limitation now.

Related closed issues: #1290, #1353.

Review the Native Windows sections in README.md, docs/guide/resources/troubleshooting.md, and docs/guide/getting-started/supported-agents.md, then compare them with src/hooks/constants.rs and src/hooks/init.rs around the cited lines. Update the stale fallback description to match the native hook behavior and note the Bash-tool-only limitation tracked in #1319; done means all listed Windows guidance is consistent.