docs: rename bot from claude-bot to claude in CI and docs

Update all runtime-relevant references to the Forgejo bot username
from 'claude-bot' to 'claude' following the bot account rename.

- .forgejo/workflows/claude.yml: bot_name input
- docs/forgejo.md: setup guide, examples, and inline references
- CLAUDE.md: bot identity description

Test fixtures and historical PRD files are left unchanged as they
use 'claude-bot' as arbitrary mock data or historical record.

Co-authored-by: vtmocanu <vtmocanu@users.noreply.github.com>

docs/forgejo.md

@@ -44,7 +44,7 @@ jobs:
           platform: "forgejo"
           github_token: ${{ secrets.CLAUDE_BOT_TOKEN }}
           bot_id: "YOUR_BOT_ID" # Replace with your bot's Forgejo user ID (see step 5 below)
-          bot_name: "claude-bot"
+          bot_name: "claude"
           bot_email: "claude@yourdomain.com" # Must match the bot user's registered email
 ```
 
@@ -72,7 +72,7 @@ jobs:
           platform: "forgejo"
           github_token: ${{ secrets.CLAUDE_BOT_TOKEN }}
           bot_id: "YOUR_BOT_ID" # Replace with your bot's Forgejo user ID
-          bot_name: "claude-bot"
+          bot_name: "claude"
           bot_email: "claude@yourdomain.com"
 ```
 
@@ -140,7 +140,7 @@ On GitHub, Claude gets its own identity via the GitHub App (`claude[bot]`). On F
 
 Creating a dedicated bot user solves this:
 
-- **Clear attribution**: Commits and comments show as `claude-bot`, not your personal account
+- **Clear attribution**: Commits and comments show as `claude`, not your personal account
 - **Least privilege**: The bot token has only the permissions Claude needs
 - **Audit trail**: Easy to distinguish human actions from bot actions in repo history
 - **Security**: If the action is compromised, only the bot's scoped token is exposed
@@ -151,7 +151,7 @@ Creating a dedicated bot user solves this:
 
 Go to **Site Administration > User Accounts > Create User Account** or use the admin API:
 
-- **Username**: `claude-bot`
+- **Username**: `claude`
 - **Email**: e.g., `claude@yourdomain.com`
 - **Password**: any strong password (you'll use API tokens, not password login)
 - **Uncheck** "Require user to change password"
@@ -166,11 +166,11 @@ For each organization where Claude should operate:
 2. Create a team named `Claude` with:
    - **Permission**: `Write`
    - **Access**: All Repositories (so new repos are automatically covered)
-3. Add `claude-bot` to the team's **Members**
+3. Add `claude` to the team's **Members**
 
 #### 3. Generate a scoped API token
 
-Log in as `claude-bot`, go to **Settings > Applications**, and create a token:
+Log in as `claude`, go to **Settings > Applications**, and create a token:
 
 - **Token Name**: `claude-code-action`
 - **Scopes**:
@@ -187,7 +187,7 @@ Add the token as `CLAUDE_BOT_TOKEN` at the **organization level** (Settings > Ac
 You'll need the Forgejo user ID for the `bot_id` input:
 
 ```bash
-curl -s "https://your-forgejo-instance/api/v1/users/claude-bot" | jq '.id'
+curl -s "https://your-forgejo-instance/api/v1/users/claude" | jq '.id'
 ```
 
 #### 6. Configure the workflow
@@ -199,7 +199,7 @@ curl -s "https://your-forgejo-instance/api/v1/users/claude-bot" | jq '.id'
     platform: "forgejo"
     github_token: ${{ secrets.CLAUDE_BOT_TOKEN }}
     bot_id: "YOUR_BOT_ID" # Replace with the ID from step 5
-    bot_name: "claude-bot"
+    bot_name: "claude"
     bot_email: "claude@yourdomain.com" # Must match the bot user's registered email
 ```
 
@@ -210,7 +210,7 @@ The `bot_email` input overrides the default noreply email format. When it matche
 Forgejo API tokens can expire. Plan for rotation:
 
 1. **Set a calendar reminder** for before the token expires
-2. **Generate a new token** by logging in as `claude-bot` (same scopes as above)
+2. **Generate a new token** by logging in as `claude` (same scopes as above)
 3. **Update the org secret** `CLAUDE_BOT_TOKEN` with the new token value
 4. **No code changes needed** — the workflow reads the secret at runtime