If I understand right, persistent HOME and/or OPT mean that HOME and/or OPT files are written to your save device (e.g. hard disk or USB stick) whenever the files are modified while TCL is running.
If you don't have persistent HOME or OPT, the file modifications are in RAM only and aren't saved until the backup when you shutdown. This is how my box is because I want to minimize writes to the USB stick.
The copy2fs.flg and copy2fs.list files only affect extensions and don't change how the basic OS works.
Is this correct?
Yes this is correct
Persistent home and opt, only affect files in /home and /opt, and are written to when a file is modified.
Backup only affects files in backup, and this is only written to when backup is performed, normally when shutting down.
copy2fs.flg and copy2fs.list files only affect whether extensions are mounted or loaded to ram when the computer is started.