Hey @Jason83, my apologies for the very delayed reply - thank you in advance for your patience! I wanted to jump on and ensure I got back to you incase you still were looking for an answer here.
At this point, there isn’t an action specific section within permissions as you would’ve come to realise. That said, if users have the override permissions: manage all data, you will be able to delete your own actions. For more in-depth action settings regarding editing certain detail fields and visibility, check out this article → https://help.safetyculture.com/en-US/001908/
In terms of logs for actions, you should be able to see this in the activity log of the organisation, within the organisation settings. Here you can see who deleted an action, what action it was and when, however it isn’t possible to retrieve it I am afraid as deletion of an action is permanent. Apologies in advance for the inconvenience caused here
Let me know if you have any questions!