I agree the root cause here is the lack of a primary key to begin with. But as far as I know, DDL is always replicated as just a statement, regardless of session binlog_format. So I believe the only real fix here is the general approach suggested in the manual [1], i.e. create a new empty table that has the auto_increment PK added and then populate it from the old table.
[1] https://dev.mysql.com/doc/refman/9.7/en/replication-features...