Split IdentifierId and StringLiteralId from StringId (#3352)

Following up on discussion yesterday regarding this split.

Note, I'm expecting #3341 to do IdentifierId -> NameId in SemIR. It
might be worth adding NameId creation directly to StringStore if you're
content with this setup though.

toolchain/check/handle_function.cpp

@@ -101,7 +101,7 @@ static auto BuildFunctionDeclaration(Context& context, bool is_definition)
         {.name_id = name_context.state ==
                             DeclarationNameStack::NameContext::State::Unresolved
                         ? name_context.unresolved_name_id
-                        : StringId::Invalid,
+                        : IdentifierId::Invalid,
          .implicit_param_refs_id = implicit_param_refs_id,
          .param_refs_id = param_refs_id,
          .return_type_id = return_type_id,
@@ -174,7 +174,7 @@ auto HandleFunctionDefinitionStart(Context& context, Parse::Node parse_node)
                       "Previous definition was here.");
     context.emitter()
         .Build(parse_node, FunctionRedefinition,
-               context.strings().Get(function.name_id))
+               context.identifiers().Get(function.name_id))
         .Note(context.insts().Get(function.definition_id).parse_node(),
               FunctionPreviousDefinition)
         .Emit();
@@ -212,9 +212,9 @@ auto HandleFunctionDefinitionStart(Context& context, Parse::Node parse_node)
       // TODO: This will shadow a local variable named `r#self`, but should
       // not. See #2984 and the corresponding code in
       // HandleSelfTypeNameExpression.
-      context.AddNameToLookup(self_param->parse_node,
-                              context.strings().Add(SemIR::SelfParameter::Name),
-                              param_id);
+      context.AddNameToLookup(
+          self_param->parse_node,
+          context.identifiers().Add(SemIR::SelfParameter::Name), param_id);
     } else {
       CARBON_FATAL() << "Unexpected kind of parameter in function definition "
                      << param;
@@ -244,8 +244,8 @@ auto HandleReturnType(Context& context, Parse::Node parse_node) -> bool {
   auto type_id = ExpressionAsType(context, type_parse_node, type_inst_id);
   // TODO: Use a dedicated instruction rather than VarStorage here.
   context.AddInstAndPush(
-      parse_node,
-      SemIR::VarStorage{parse_node, type_id, context.strings().Add("return")});
+      parse_node, SemIR::VarStorage{parse_node, type_id,
+                                    context.identifiers().Add("return")});
   return true;
 }