It does say it persists through death. It also says that the only way to remove them is with RemoveEffect. Yeah just not sure how/if it saves in a different way than the other similar effects like supernatural. Was hoping it was a way to not have to worry about re-applying them.
One way to make an effect seemingly persist through resets is to modify the script which applies the effect so that it leaves a variable on an undroppable object in the player's inventory, then use the OnClientEnter script to check for that variable and have the script re-apply the effect. If the effect is ever removed, then whatever script removes it needs to also remove the variable so that the effect does not get re-applied on enter.
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I would guess that no effects remain across server resets: seeing that even supernatural and extraordinary effects have to be re-applied.
Darn. Thank you for the info.