feat: inject global rules into AI system prompt and fix Rules UI seeding

- Load global rules (AIFact/AIMemory) from local CloudModel and inject
  them into the Bedrock/OpenAI system prompt as a '## Global Rules' section
  when memory is enabled.
- Fix rule seeding: always re-seed predefined rules when the CloudModel has
  none, regardless of the has_seeded_predefined_rules flag (handles case
  where flag was set but rules never persisted due to prior missing owner).
- Rename /context slash command to /copy-context: dumps the full context
  window (global rules, progressive summary, message history) to the
  clipboard for debugging.

app/src/ai/bedrock/e2e_tests.rs

@@ -1890,7 +1890,7 @@ async fn test_full_proto_round_trip_with_tool_history() {
     );
 
     let messages = super::request_translator::extract_messages_from_request(&request);
-    let system_prompt = super::request_translator::extract_system_prompt(&request);
+    let system_prompt = super::request_translator::extract_system_prompt(&request, &[]);
     let tools = super::request_translator::extract_tools(&request);
 
     println!("\n=== FULL PROTO ROUND-TRIP TEST ===");

app/src/ai/bedrock/request_translator.rs

@@ -954,7 +954,7 @@ fn collect_tool_result_ids(content: &MessageContent, ids: &mut std::collections:
     }
 }
 
-pub fn extract_system_prompt(request: &api::Request) -> Option<String> {
+pub fn extract_system_prompt(request: &api::Request, global_rules: &[(String, String)]) -> Option<String> {
     let mut prompt = String::with_capacity(2048);
 
     prompt.push_str("You are Galaxy, an AI coding assistant embedded in a terminal application. You help users with software engineering tasks including writing code, debugging, explaining concepts, and navigating codebases.\n\n");
@@ -1009,6 +1009,19 @@ pub fn extract_system_prompt(request: &api::Request) -> Option<String> {
         }
     }
 
+    // Inject global rules from the local CloudModel (stored as AIFact/AIMemory)
+    if !global_rules.is_empty() {
+        prompt.push_str("## Global Rules\n");
+        prompt.push_str("The following rules have been configured by the user and should be followed:\n\n");
+        for (name, content) in global_rules {
+            if !name.is_empty() {
+                prompt.push_str(&format!("### {}\n", name));
+            }
+            prompt.push_str(content);
+            prompt.push_str("\n\n");
+        }
+    }
+
     prompt.push_str("## Tool Usage\n");
     prompt.push_str("You have been given every tool you need to complete your tasks. Use them to achieve results with as few calls and as little back-and-forth as possible.\n\n");
     prompt.push_str("**How to choose tools:**\n");

app/src/ai/bedrock/translator.rs

@@ -18,6 +18,8 @@ pub struct TranslatorRequest {
     pub bedrock_tool_result_archive: Vec<ConversationMessage>,
     pub bedrock_progressive_summary: Option<String>,
     pub bedrock_messages_sent: Arc<Mutex<Vec<ConversationMessage>>>,
+    /// Global rules (name, content) from the local CloudModel.
+    pub global_rules: Vec<(String, String)>,
 }
 
 pub async fn execute(
@@ -104,7 +106,7 @@ pub async fn execute(
 
     request_translator::sanitize_messages_for_bedrock(&mut messages);
 
-    let system_prompt = request_translator::extract_system_prompt(request);
+    let system_prompt = request_translator::extract_system_prompt(request, &params.global_rules);
     let tools = request_translator::extract_tools(request);
 
     log::info!(