docs: rename patch tool to apply_patch and clarify apply_patch behavior (#19979)

Author: yejiming

packages/web/src/content/docs/tools.mdx

@@ -95,7 +95,7 @@ Create new files or overwrite existing ones.
 Use this to allow the LLM to create new files. It will overwrite existing files if they already exist.
 
 :::note
-The `write` tool is controlled by the `edit` permission, which covers all file modifications (`edit`, `write`, `patch`, `multiedit`).
+The `write` tool is controlled by the `edit` permission, which covers all file modifications (`edit`, `write`, `apply_patch`, `multiedit`).
 :::
 
 ---
@@ -191,7 +191,7 @@ To configure which LSP servers are available for your project, see [LSP Servers]
 
 ---
 
-### patch
+### apply_patch
 
 Apply patches to files.
 
@@ -206,8 +206,12 @@ Apply patches to files.
 
 This tool applies patch files to your codebase. Useful for applying diffs and patches from various sources.
 
+When handling `tool.execute.before` or `tool.execute.after` hooks, check `input.tool === "apply_patch"` (not `"patch"`).
+
+`apply_patch` uses `output.args.patchText` instead of `output.args.filePath`. Paths are embedded in marker lines within `patchText` and are relative to the project root (for example: `*** Add File: src/new-file.ts`, `*** Update File: src/existing.ts`, `*** Move to: src/renamed.ts`, `*** Delete File: src/obsolete.ts`).
+
 :::note
-The `patch` tool is controlled by the `edit` permission, which covers all file modifications (`edit`, `write`, `patch`, `multiedit`).
+The `apply_patch` tool is controlled by the `edit` permission, which covers all file modifications (`edit`, `write`, `apply_patch`, `multiedit`).
 :::
 
 ---