The labels are indeed wrong. Technically, marking a file as safe/unsafe is a publish/unpublish action and uses the same code in Joomla. We just put a different label. Despite the wrong label appearing in the menu the feature works fine.
Regarding Mark all as safe, clicking the button in all of the sites I have (development, testing, and live) takes under 2 seconds. This is expected since we do a mass update query instead of updating each item individually. Clicking the icon in the Marked Safe column also takes under a second, but it only updates a single record. Selecting a lot of records and then going to Actions, Publish/Unpublish takes substantially longer as each selected item is marked safe/unsafe individually. Since Admin Tools is a Joomla component, the Joomla framework runs content and system plugin actions for each item marked safe/unsafe. Some third party plugins may take several hundreds of milliseconds to a few seconds per item. If it's about 50 to 60 milliseconds per item, multiplied by 5000 items you get about 300 seconds i.e. 5 minutes.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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