In your usecase, the ideal way to setup would be
1. In your content tab, check the box that says "Backup only when qualified for archiving"
2. In the disk clean up tab, you can set the rule as modified time older than 3 months
3. In your subclient retention tab (under advanced), you can choose
Extend Storage Policy retention checkox should be ON
archive retention can be set to 6 months
Backup retention should be OFF
This would mean that your files will be in CV archives for 6 months and after 6 months it would get aged off. Once its aged off of CV archives, the stubs on disk cannot be recalled/restored. Your Storage policy retention of 183 days is fine.
Pruning happens automatically here where the stubs are removed from the disk after 6 months once it ages off from CV archives.
You will not need synthetic full to support this use case. Hope you have not already run synthetic full yet on this subclient. If you have, please let us know and we can direct you accordingly.
Finally, a note - this configuration is only for archiving. Please have a seperate backupset and configure it for backup of regular data that does not meet archiving rules.
Please let us know if you have any questions.