Where FormatSettings is the TFormatSettings(https://www.freepascal.org/docs-html/rtl/sysutils/tformatsettings.html) it has nothing to do with JEDI format settings/registry.
Sorry but your diagnosis is wrong. For some reason JEDI named their options class as "TFormatSettings" and a function "FormatSettings". It is extremely confusing especially because the same unit frFiles also uses DefaultFormatSettings from Sysutils.
It must be changed ... and so I did in r55493. It is now "
FormattingSettings".
In my tests the new option is not persistent. I turn it off, then restart Lazarus and it is on again.
Restoring the backslash to OLD_REG_ROOT_KEY makes no difference. No errors but still not persistent.
Tested in Linux. The code uses TRegIniFile which is cross-platform.
IMO this looks wrong without backslash:
OLD_REG_ROOT_KEY = 'Software\Jedi\JediCodeFormat';
Every other registry path has the leading backslash.
The package has JcfSettings which uses JcfRegistrySettings. It is not straightforward.
Can you please take a look.