Can I emulate Oracle's autonomous transaction in MySQL?
If you have access to the Aria engine or another non-transactional engine, then yes.
Very short proof of concept, tested on MariaDB 10.5.4:
CREATE TABLE test_aria_engine ( a int, b varchar(1000) )
ENGINE=Aria DEFAULT CHARSET=utf8 PAGE_CHECKSUM=1 TRANSACTIONAL=1 TABLE_CHECKSUM=1
COMMENT='test-aria_engine with transactional on 1'

The transactional in Aria is not for real transactions, it is only last operation log, still good in case of server crash the data is consistent.
Now create an InnoDB table:
CREATE TABLE test_innodb_engine ( a int , b varchar(1000) )

And test:
BEGIN TRANSACTION;

-- insert in aria table
INSERT INTO test_aria_engine ( a, b) VALUES (4 , 'ddd');

-- insert in innodb table
INSERT INTO test_innodb_engine( a, b) VALUES ( 4 , 'dddd');

-- rollback
ROLLBACK;

After the ROLLBACK has been initiated let's check the table contents of the Aria and InnoDB tables:
SELECT * FROM test_aria_engine;


|a  |b  |
|---|---|
|4  |ddd|


So, ROLLBACK cannot rollback ARIA engine
SELECT * FROM test_innodb_table;


No result.


So in the InnoDB table ROLLBACK has done its job.
This shows how to avoid transaction logic in MariaDB or using a similar engine like MyISAM in MySQL.