refactor(joinir): Extract legacy binding path to routing_legacy_binding.rs

Phase 179-A Step 2: Separate LoopFrontendBinding JSON construction logic
into dedicated module for better organization.

Changes:
- New file: routing_legacy_binding.rs (223 lines)
- routing.rs: cf_loop_joinir_impl() simplified to 15 lines (delegates to legacy path)
- Routing now clearly separates pattern-based vs. legacy binding paths

Benefits:
- Clear separation of concerns (pattern router vs. legacy whitelist)
- routing.rs reduced from 364 to 146 lines (60% reduction)
- Legacy path isolated for future deprecation

src/mir/join_ir/lowering/loop_update_analyzer.rs

@@ -38,10 +38,20 @@ pub enum UpdateExpr {
 }
 
 /// Right-hand side of update expression
+///
+/// Phase 178: Extended to detect string updates for multi-carrier loops.
+/// The goal is "carrier detection", not full semantic understanding.
 #[derive(Debug, Clone)]
 pub enum UpdateRhs {
+    /// Numeric constant: count + 1
     Const(i64),
+    /// Variable reference: sum + i
     Variable(String),
+    /// Phase 178: String literal: result + "x"
+    StringLiteral(String),
+    /// Phase 178: Other expression (method call, complex expr)
+    /// Used to detect "carrier has an update" without understanding semantics
+    Other,
 }
 
 pub struct LoopUpdateAnalyzer;
@@ -157,6 +167,9 @@ impl LoopUpdateAnalyzer {
     }
 
     /// Analyze right-hand side of update expression
+    ///
+    /// Phase 178: Extended to detect string updates.
+    /// Goal: "carrier has update" detection, not semantic understanding.
     fn analyze_rhs(node: &ASTNode) -> Option<UpdateRhs> {
         match node {
             // Constant: count + 1
@@ -165,11 +178,24 @@ impl LoopUpdateAnalyzer {
                 ..
             } => Some(UpdateRhs::Const(*n)),
 
-            // Variable: sum + i
+            // Phase 178: String literal: result + "x"
+            ASTNode::Literal {
+                value: LiteralValue::String(s),
+                ..
+            } => Some(UpdateRhs::StringLiteral(s.clone())),
+
+            // Variable: sum + i (also handles: result + ch)
             ASTNode::Variable { name, .. } => {
                 Some(UpdateRhs::Variable(name.clone()))
             }
 
+            // Phase 178: Method call or other complex expression
+            // e.g., result + s.substring(pos, end)
+            ASTNode::Call { .. }
+            | ASTNode::MethodCall { .. }
+            | ASTNode::BinaryOp { .. }
+            | ASTNode::UnaryOp { .. } => Some(UpdateRhs::Other),
+
             _ => None,
         }
     }
@@ -218,6 +244,7 @@ mod tests {
         let carriers = vec![CarrierVar {
             name: "count".to_string(),
             host_id: crate::mir::ValueId(0),
+            join_id: None, // Phase 177-STRUCT-1
         }];
 
         let updates = LoopUpdateAnalyzer::analyze_carrier_updates(&body, &carriers);