Automate clearing Safari history?

You can set up a shortcut that will take you to the option to clear Safari's cache:

https://www.ojisanseiuchi.com/2020/10/10/ios-shortcut-to-clear-safari/

but that just will take you to the screen. You then have to clear the cache yourself. I don't know of any way to completely automate it. I just tell Siri to clear Safari's cache so it at least eliminates all the tapping to get to that screen.

Regards.

I suppose, it "may" be possible to create a shortcut and use the action button to run the shortcut.

Here is how to create shortcuts for the Action Button --> Shortcuts User Guide - Apple Support

And this about using the Action Button --> Use and customize the Action button on iPhone - Apple Support

You're welcome.