feat: update to use core tap for beads installation (#1261)

* feat: update to use core tap for beads installation

Signed-off-by: Rui Chen <rui@chenrui.dev>

* remove custom tap related code and refs

Signed-off-by: Rui Chen <rui@chenrui.dev>

---------

Signed-off-by: Rui Chen <rui@chenrui.dev>

website/docs/getting-started/installation.md

@@ -13,8 +13,7 @@ Complete installation guide for all platforms.
 ### Homebrew (macOS/Linux)
 
 ```bash
-brew tap steveyegge/beads
-brew install bd
+brew install beads
 ```
 
 **Why Homebrew?**
@@ -41,8 +40,7 @@ The installer will:
 
 **Via Homebrew** (recommended):
 ```bash
-brew tap steveyegge/beads
-brew install bd
+brew install beads
 ```
 
 **Via go install**:
@@ -62,8 +60,7 @@ sudo mv bd /usr/local/bin/
 
 **Via Homebrew** (works on Linux too):
 ```bash
-brew tap steveyegge/beads
-brew install bd
+brew install beads
 ```
 
 **Arch Linux** (AUR):
@@ -117,7 +114,7 @@ The recommended approach for Claude Code, Cursor, Windsurf, and other editors wi
 
 ```bash
 # 1. Install bd CLI (see Quick Install above)
-brew install bd
+brew install beads
 
 # 2. Initialize in your project
 cd your-project

website/docs/intro.md

@@ -23,8 +23,7 @@ Traditional issue trackers (Jira, GitHub Issues) weren't designed for AI agents.
 
 ```bash
 # Install via Homebrew (macOS/Linux)
-brew tap steveyegge/beads
-brew install bd
+brew install beads
 
 # Or quick install (macOS/Linux/FreeBSD)
 curl -fsSL https://raw.githubusercontent.com/steveyegge/beads/main/scripts/install.sh | bash