How to myke the MySQL Slow Query Log respect the long_query_time?

Question

My Slow Query Log is full of queries, that should not be written there, e.g.:

# Time: 2022-03-11T12:23:29.258308Z
# User@Host: ...
# Schema: ...
# Query_time: 0.022791  Lock_time: 0.000201  Rows_sent: 1000  Rows_examined: 1000  Rows_affected: 0  Bytes_sent: 115518
use ...;
SET timestamp=1647001409;
SELECT * FROM `my_table` LIMIT 0,1000;

The query time is 0.022791 seconds. And the long_query_time is 5.000000:

mysql> SHOW VARIABLES WHERE `variable_name` = "long_query_time";
+-----------------+----------+
| Variable_name   | Value    |
+-----------------+----------+
| long_query_time | 5.000000 |
+-----------------+----------+

What's going wrong here? How to avoid such a "spam" in the Slow Query Log?

mysql> SELECT VERSION();
+---------------+
| VERSION()     |
+---------------+
| 5.7.36-39-log |