Deleted Messages conversations inconsistent between devices

OSX native messaging app is set to Sync via iCloud account. Messages sent on either device (iPhone/Macbook) DO sync without issue.

Deleting a conversation via Macbook will present the following message:

This insinuates that the deleted conversation will be removed from my iPhone, however, this is not the case! (The same is true when deleting from iPhone)

Comparing meessages on iPhone and Macbook, you can see many inconsistencies:

My desired outcome is to have conversations within Messages mirror on all devices.

If I delete a convo on iPhone I expect it to be deleted on Macbook.

If I delete a convo on Macbook I expect it to be deleted on iPhone.

I have tried logging in/out of my iCloud account on both devices to no avail.

iPhone > Settings > Name > iCloud > Messages was not set to sync.

Setting it to Sync has resolved the issue.