Rename Builtin to BuiltinInst, particularly to get BuiltinInstKind (#4115)

I'm trying to increase the distinction between BuiltinKind and
BuiltinFunctionKind. BuiltinKind is for instructions,
BuiltinFunctionKind is for function definitions. To get to this point,
I'm doing a few changes:

- BuiltinKind -> BuiltinInstKind
    - builtin_kind.* -> builtin_inst_kind.*: filename consistency
- Builtin -> BuiltinInst: mainly for consistency with the above
- Builtin::builtin_kind -> BuiltinInst::builtin_inst_kind: somewhat
repetitive but seems like a consistent edit
- Function::builtin_kind -> Function::builtin_function_kind: seems a
useful distinction

I'm leaving alone things like (and mentioning in case there's a desire
for more renames):

- InstId::BuiltinError, InstId::ForBuiltin: these I think are more
apparent because they're directly associated with Inst.
- GetBuiltinICmpPredicate in lowering: maybe builtin function handling
should be in its own file, but these local names don't feel problematic
to me.
- GetBuiltinType, BuildBuiltinValueRepr, PerformBuiltinIntComparison:
similar to the above, names don't feel too problematic

toolchain/check/handle_function.cpp

@@ -313,7 +313,7 @@ static auto BuildFunctionDecl(Context& context,
         !context.inst_blocks().Get(function_info.param_refs_id).empty() ||
         (return_type_id.is_valid() &&
          return_type_id !=
-             context.GetBuiltinType(SemIR::BuiltinKind::IntType) &&
+             context.GetBuiltinType(SemIR::BuiltinInstKind::IntType) &&
          return_type_id != context.GetTupleType({}))) {
       CARBON_DIAGNOSTIC(InvalidMainRunSignature, Error,
                         "Invalid signature for `Main.Run` function. Expected "
@@ -474,7 +474,7 @@ static auto LookupBuiltinFunctionKind(Context& context,
 }
 
 // Returns whether `function` is a valid declaration of the builtin
-// `builtin_kind`.
+// `builtin_inst_kind`.
 static auto IsValidBuiltinDeclaration(Context& context,
                                       const SemIR::Function& function,
                                       SemIR::BuiltinFunctionKind builtin_kind)
@@ -514,7 +514,7 @@ auto HandleBuiltinFunctionDefinition(
   if (builtin_kind != SemIR::BuiltinFunctionKind::None) {
     auto& function = context.functions().Get(function_id);
     if (IsValidBuiltinDeclaration(context, function, builtin_kind)) {
-      function.builtin_kind = builtin_kind;
+      function.builtin_function_kind = builtin_kind;
     } else {
       CARBON_DIAGNOSTIC(InvalidBuiltinSignature, Error,
                         "Invalid signature for builtin function \"{0}\".",