There is a couple of things going on here. I suspect there is more than one scenario which can cause this.
In my case, I deleted a device. That same device was in an automation with a Device action. The frontend - unbeknownst to me - clears any invalid, or in this case non-existent, device_id’s from the Device action’s. When I click save on the automation from the UI, it then sends the empty Device action to the core. By this point, three errors have been generated. The last of which is shown - Integration '' not found.
I have raised a frontend bug here When device is deleted, automation UI fails to clear references to that device cleanly · Issue #19694 · home-assistant/frontend · GitHub.
If you are still facing this issue, I encourage you to go thumbs up on that bug.