Separate binding insts for refs and values (#6235)

This resolves a TODO in `expr_info.cpp` by using the inst kind rather
than the bound value to track the binding's category.

Since we're churning all the `bind_name` insts in testdata anyway, I'm
also taking this opportunity to align the inst naming with the design's
terminology, by calling these insts "bindings" (this aspect of the PR is
dependent on #6231 resolving an ambiguity in that terminology). For
consistency we'll need to rename several other insts as well (see the
TODO on `RefBinding`); I'm deferring that to a separate PR to minimize
the review load, but I think those name changes are in-scope for this
review.

toolchain/check/handle_binding_pattern.cpp

@@ -47,6 +47,21 @@ static auto HandleAnyBindingPattern(Context& context, Parse::NodeId node_id,
   // A non-generic template binding is diagnosed by the parser.
   is_template &= is_generic;
 
+  SemIR::InstKind pattern_inst_kind;
+  switch (node_kind) {
+    case Parse::NodeKind::CompileTimeBindingPattern:
+      pattern_inst_kind = SemIR::InstKind::SymbolicBindingPattern;
+      break;
+    case Parse::NodeKind::LetBindingPattern:
+      pattern_inst_kind = SemIR::InstKind::ValueBindingPattern;
+      break;
+    case Parse::NodeKind::VarBindingPattern:
+      pattern_inst_kind = SemIR::InstKind::RefBindingPattern;
+      break;
+    default:
+      CARBON_FATAL("Unexpected node kind: {0}", node_kind);
+  }
+
   auto [name_node, name_id] = context.node_stack().PopNameWithNodeId();
 
   const DeclIntroducerState& introducer =
@@ -57,7 +72,7 @@ static auto HandleAnyBindingPattern(Context& context, Parse::NodeId node_id,
     // scopes, but right now we don't support qualified names here.
     auto binding =
         AddBindingPattern(context, name_node, name_id, cast_type_id,
-                          type_expr_region_id, is_generic, is_template);
+                          type_expr_region_id, pattern_inst_kind, is_template);
 
     // TODO: If `is_generic`, then `binding.bind_id is a BindSymbolicName. Subst
     // the `.Self` of type `type` in the `cast_type_id` type (a `FacetType`)