docs: fix 6 documentation issues (#303, #245, #186, #134, #61, #73) (#486)

* docs: fix 6 documentation issues (#303, #245, #186, #134, #61, #73)

Addresses six open documentation issues in a single pass:

- **#303** -- Add `npx agent-browser` usage across README, SKILL.md, docs site, and `--help` output for zero-install experience. Global install is recommended as the fastest path (native Rust CLI vs Node.js indirection with npx).
- **#245** -- Document Claude Code skill installation with `npx skills add vercel-labs/agent-browser`
- **#186** -- Split installation instructions into Global (recommended), Quick Start (npx), and Project (local dependency) sections with clear guidance on when to use each
- **#134** -- Add "Why agent-browser over playwright-mcp?" comparison table to README covering output format, element selection, protocol, sessions, performance, mobile, cloud, and streaming
- **#61** -- Add "Timeouts and Slow Pages" section to SKILL.md documenting the 60s default timeout, all `wait` variants, and guidance for slow websites
- **#73** -- Replace stale `cp node_modules/...` advice with `npx skills add`, add warning against copying SKILL.md manually, add "Session Management and Cleanup" section to SKILL.md

* remove section

* fix doc

docs/src/app/installation/page.mdx

@@ -2,13 +2,43 @@ export const metadata = { title: "Installation" }
 
 # Installation
 
-## npm (recommended)
+## Global installation (recommended)
+
+Installs the native Rust binary for maximum performance:
 
 ```bash
 npm install -g agent-browser
 agent-browser install  # Download Chromium
 ```
 
+This is the fastest option -- commands run through the native Rust CLI directly with sub-millisecond parsing overhead.
+
+## Quick start (no install)
+
+Run directly with `npx` if you want to try it without installing globally:
+
+```bash
+npx agent-browser install   # Download Chromium (first time only)
+npx agent-browser open example.com
+```
+
+> **Note:** `npx` routes through Node.js before reaching the Rust CLI, so it is noticeably slower than a global install. For regular use, install globally.
+
+## Project installation (local dependency)
+
+For projects that want to pin the version in `package.json`:
+
+```bash
+npm install agent-browser
+npx agent-browser install
+```
+
+Then use via `npx` or `package.json` scripts:
+
+```bash
+npx agent-browser open example.com
+```
+
 ## Homebrew (macOS)
 
 ```bash
@@ -73,6 +103,18 @@ export async function handler() {
 
 agent-browser works with any AI agent out of the box. For richer context:
 
+### AI coding assistants (recommended)
+
+Install the skill for your AI coding assistant:
+
+```bash
+npx skills add vercel-labs/agent-browser
+```
+
+This works with Claude Code, Codex, Cursor, Gemini CLI, GitHub Copilot, Goose, OpenCode, and Windsurf. The skill is fetched from the repository and stays up to date automatically.
+
+> **Do not** copy `SKILL.md` from `node_modules` -- it will become stale as new features are added. Always use `npx skills add` or reference the repository version.
+
 ### AGENTS.md / CLAUDE.md
 
 Add to your instructions file:
@@ -88,17 +130,3 @@ Core workflow:
 3. `agent-browser click @e1` / `fill @e2 "text"` - Interact using refs
 4. Re-snapshot after page changes
 ```
-
-### Claude Code skill
-
-```bash
-cp -r node_modules/agent-browser/skills/agent-browser .claude/skills/
-```
-
-Or download:
-
-```bash
-mkdir -p .claude/skills/agent-browser
-curl -o .claude/skills/agent-browser/SKILL.md \
-  https://raw.githubusercontent.com/vercel-labs/agent-browser/main/skills/agent-browser/SKILL.md
-```

docs/src/app/page.mdx

@@ -5,8 +5,11 @@ export const metadata = { title: "agent-browser" }
 Browser automation CLI designed for AI agents. Compact text output minimizes context usage. Fast Rust CLI with Node.js fallback.
 
 ```bash
-npm install -g agent-browser      # all platforms
+npm install -g agent-browser      # all platforms (fastest, native Rust CLI)
 brew install agent-browser        # macOS
+
+# or try without installing
+npx agent-browser open example.com
 ```
 
 ## Features