Local recording is in fact currently the only option, you're forced to buy one of their assorted NVR devices to use Ubiquiti's cameras.

(Technically it could be in another location streaming from the camera to the NVR across the internet, but you're still obliged to control both ends of that equation)

You can optionally have remote access either through Ubiquiti (which judging by the question I'm assuming you would not want) or by your own VPN or other self-controlled method.

There's also good integration with Home Assistant, which you can use for notifications based on motion detection or other events. I use that method for my doorbell, playing an mp3 out of one of the speakers in the house, due to the lack of any actual doorbell chime. They'll also sell you a PoE-powered chime that links to the NVR though.