How do I delete all images from "All Photos" library in Lightroom

If your workflow is to import images into Lightroom Cloud ecosystem and then delete them from the cloud after editing and saving the finished images, you might want to consider using Lightroom Classic or perhaps even more appropriate Adobe Bridge together with Camera Raw instead.  This is not a workflow that is very compatible with the cloud application.

You should also be able to delete your whole Library from Library from http://lightroom.adobe.com/ as outlined in this thread:

https://community.adobe.com/t5/lightroom-ecosystem-cloud-based-discussions/delete-all-files-on-cloud/m-p/9424565#M1170

This will clear everything and I don't think there is a way of reversing this, so as per Johan's concerns, ensure you definitely no longer require anything in the Cloud and that everything is backed up.

If you delete all the images in 'All Photos', then you will delete these images and their edits from Lightroom altogether. That means you will lose all the work you've done on these images, unless you have exported them first. Is that really what you want? 

If that is really what you want, then read this: https://community.adobe.com/t5/lightroom-ecosystem-cloud-based-bugs/p-deleted-photos-not-being-deleted-in-lightroom/idi-p/13686668