fix: remove duplicate git validation logic in exec module

- Remove redundant git validation block at lines 213-222
- Keep only the consolidated implementation that reuses git_repo_root result
- Eliminates duplicate get_git_repo_root() calls for better performance
- Maintains DRY principles and code quality
- Addresses critical issue identified in merge commit 086980b

Fixes: Duplicate code issue from merge conflict resolution

Author: boice-sealint

codex-rs/exec/src/lib.rs

@@ -210,17 +210,6 @@ pub async fn run_main(cli: Cli, codex_linux_sandbox_exe: Option<PathBuf>) -> any
         }
     }
 
-    // If inside a git repo but with no commits, provide a clearer message.
-    if !skip_git_repo_check
-        && get_git_repo_root(&config.cwd.to_path_buf()).is_some()
-        && !codex_core::git_info::git_repo_has_commits(&config.cwd).await
-    {
-        eprintln!(
-            "This Git repository has no commits. Initialize it first:\n  git add -A && git commit -m 'Initial commit'\nOr pass --skip-git-repo-check to bypass."
-        );
-        std::process::exit(1);
-    }
-
     let conversation_manager =
         ConversationManager::new(AuthManager::shared(config.codex_home.clone()));