feat: add bot_id input to handle GitHub App authentication errors (#534)

Adds a new optional bot_id input parameter that defaults to the github-actions[bot] ID (41898282). This resolves the "403 Resource not accessible by integration" error that occurs when using GitHub App installation tokens, which cannot access the /user endpoint.

Changes:
- Add bot_id input to action.yml with default value
- Update context parsing to include bot_id from environment
- Modify agent mode to use bot_id when available, avoiding API calls that fail with GitHub App tokens
- Add clear error handling for GitHub App token limitations
- Update documentation in usage.md and faq.md
- Fix test mocks to include bot_id field

This allows users to specify a custom bot user ID or use the default github-actions[bot] ID automatically, preventing 403 errors in automation workflows.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Claude <noreply@anthropic.com>

src/github/operations/git-config.ts

@@ -17,7 +17,7 @@ type GitUser = {
 export async function configureGitAuth(
   githubToken: string,
   context: GitHubContext,
-  user: GitUser | null,
+  user: GitUser,
 ) {
   console.log("Configuring git authentication for non-signing mode");
 
@@ -28,20 +28,14 @@ export async function configureGitAuth(
       ? "users.noreply.github.com"
       : `users.noreply.${serverUrl.hostname}`;
 
-  // Configure git user based on the comment creator
+  // Configure git user
   console.log("Configuring git user...");
-  if (user) {
-    const botName = user.login;
-    const botId = user.id;
-    console.log(`Setting git user as ${botName}...`);
-    await $`git config user.name "${botName}"`;
-    await $`git config user.email "${botId}+${botName}@${noreplyDomain}"`;
-    console.log(`✓ Set git user as ${botName}`);
-  } else {
-    console.log("No user data in comment, using default bot user");
-    await $`git config user.name "github-actions[bot]"`;
-    await $`git config user.email "41898282+github-actions[bot]@${noreplyDomain}"`;
-  }
+  const botName = user.login;
+  const botId = user.id;
+  console.log(`Setting git user as ${botName}...`);
+  await $`git config user.name "${botName}"`;
+  await $`git config user.email "${botId}+${botName}@${noreplyDomain}"`;
+  console.log(`✓ Set git user as ${botName}`);
 
   // Remove the authorization header that actions/checkout sets
   console.log("Removing existing git authentication headers...");