feat: add background_process tool for launching long-running processes

Adds a new tool that allows launching processes (like game servers) in the
background while g3 continues to operate. The process runs independently
with stdout/stderr captured to a log file.

Features:
- Named process tracking for easy reference
- Automatic log capture to logs/background_processes/
- Returns PID and log file path for use with shell tool
- Automatic cleanup on agent shutdown via Drop trait

Usage: Use shell tool to interact with the process:
- Read logs: tail -100 <logfile>
- Check status: ps -p <pid>
- Stop process: kill <pid>

Files:
- New: crates/g3-core/src/background_process.rs
- New: crates/g3-core/tests/background_process_demo_test.rs
- Modified: crates/g3-core/src/lib.rs (tool definition + handler)
- Modified: crates/g3-core/src/prompts.rs (documentation)

crates/g3-core/tests/background_process_demo_test.rs

@@ -0,0 +1,68 @@
+use g3_core::background_process::BackgroundProcessManager;
+use std::path::PathBuf;
+use std::thread;
+use std::time::Duration;
+use std::fs;
+
+#[test]
+fn demo_background_process_with_script() {
+    // Create temp directories
+    let test_dir = std::env::temp_dir().join("g3_bg_demo");
+    let _ = fs::remove_dir_all(&test_dir);
+    fs::create_dir_all(&test_dir).unwrap();
+    
+    // Create a test script
+    let script_path = test_dir.join("test.sh");
+    fs::write(&script_path, r#"#!/bin/bash
+echo "Starting..."
+for i in 1 2 3; do
+    echo "Tick $i"
+    sleep 0.5
+done
+echo "Done!"
+"#).unwrap();
+    
+    // Make executable
+    #[cfg(unix)]
+    {
+        use std::os::unix::fs::PermissionsExt;
+        fs::set_permissions(&script_path, fs::Permissions::from_mode(0o755)).unwrap();
+    }
+    
+    let log_dir = test_dir.join("logs");
+    let manager = BackgroundProcessManager::new(log_dir);
+    
+    println!("\n=== Background Process Demo ===");
+    
+    match manager.start("demo", "./test.sh", &test_dir) {
+        Ok(info) => {
+            println!("✅ Started '{}' with PID {}", info.name, info.pid);
+            println!("   Log file: {:?}", info.log_file);
+            
+            // Wait for script to produce some output
+            thread::sleep(Duration::from_millis(800));
+            
+            // Read logs
+            let logs = fs::read_to_string(&info.log_file).unwrap_or_default();
+            println!("\n📜 Logs so far:\n{}", logs);
+            
+            // Should still be running
+            assert!(manager.is_running("demo"), "Process should still be running");
+            println!("🔍 Process is running: true");
+            
+            // Wait for completion
+            thread::sleep(Duration::from_secs(2));
+            
+            // Read final logs
+            let final_logs = fs::read_to_string(&info.log_file).unwrap_or_default();
+            println!("\n📜 Final logs:\n{}", final_logs);
+            
+            assert!(final_logs.contains("Done!"), "Should have completed");
+        }
+        Err(e) => panic!("Failed to start: {}", e),
+    }
+    
+    // Cleanup
+    let _ = fs::remove_dir_all(&test_dir);
+    println!("\n✅ Demo complete!");
+}