Handler fails to trigger on Error 1049 or SQLSTATE 42000 or plain sqlexception

CREATE DEFINER=`root`@`localhost` FUNCTION `handler_func2`() RETURNS int(11)
begin
declare exit handler for sqlexception return null;
select fake_col into @a from fake_db.fake_table;
return 1;
end

CREATE DEFINER=`root`@`localhost` FUNCTION `handler_func`() RETURNS int(11)
begin
declare exit handler for sqlexception return null;
select fake_col into @a from fake_table;
return 1;
end
mysql> select handler_func();
+----------------+
| handler_func() |
+----------------+
| NULL |
+----------------+
1 row in set (0.00 sec)

mysql> show create function handler_func2\G
*************************** 1. row ***************************
 Function: handler_func2
 sql_mode: ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_ENGINE_SUBSTITUTION
 Create Function: CREATE DEFINER=`root`@`localhost` FUNCTION `handler_func2`() RETURNS int(11)
begin
declare exit handler for sqlexception return null;
select fake_col into @a from fake_db.fake_table;
return 1;
end
character_set_client: latin1
collation_connection: latin1_swedish_ci
 Database Collation: utf8mb4_0900_ai_ci
1 row in set (0.00 sec)
mysql> show databases;
+--------------------+
| Database |
+--------------------+
| information_schema |
| mysql |
| performance_schema |
| sys |
| test |
+--------------------+
6 rows in set (0.00 sec)
mysql> select handler_func2();
ERROR 1049 (42000): Unknown database 'fake_db'