Thanks for your message.
Yes, exactly as you can see: although it supports S.M.A.R.T. on both SATA and PATA, it may still not support other commands, for example the ones which should start the self test. I'm afraid if the chip does not forward the command(s) to the drives, then there is not too much to do.
In case of USB adapters/enclosures, there is no need to check/replace/improve driver, as the functionality depends only on the USB-ATA bridge chip in the device, more precisely its firmware which may (or may not) allow using some functions/commands.
Seems positive that your device provides S.M.A.R.T. data for the IDE drive too. My combo IDE+SATA converters with Innostor IS611 chip provides S.M.A.R.T. data only for SATA disks, they did not work for IDE drives (this described on this forum, eg. in this topic: https://www.hdsentinel.com/forum/viewtopic.php?f=8&t=11529&p=18363 )
So seems your device already has an updated firmware which works (at least a bit) better. Hopefully there may be further change and a firmware update will be possible for your device which can add further functions.
I'd encourage to try to contact the manufacturer (Media-Tech) and/or Innostor directly about the situation. Hopefully if they'll receive similar requests, they will improve and release an updated firmware which can help in this case.
Ps. if possible, please use Report menu -> Send test report to developer option when an IDE and SATA HDD connected to the adapter.
This way I can check how the status reported and compare with the IS611-based devices tested. This can help checking how your device works with the drives. Thanks for your attention.