I'll preface this by saying I don't know a ton about octopus brains and anesthetization, and I certainly don't know anything about human brains.
This paper is cool to me because it's the first time someone put an implant in an octopus that is as complex as this. It records X,Y, and Z location of the implant at a fine enough scale that they can track the breathing rate of the animal by using the movement of the implant, which is really impressive. It records electrical activity of the brain, and has a flashing IR light that allows the researchers to synch their electrical recordings with their behavior video. This paper is a proof-of-concept, likely laying the groundwork for more complex experiments that can be done now that we know how to record brain activity of a behaving octopus. I'm sure this group will continue to do work with implants in behaving octopus, and seeing what happens as the animals do more complex tasks. It's important to establish groundwork studies like this so that we can start asking more complicated questions of the octopus brain.
Because there isn't a way right now to know what brain activity looks like in an octopus that doesn't have a bunch of electrodes in its head, it's hard to know if the recordings they got here are similar to those of an un-sedated, un-implanted octopus. I'm sure people have done these kinds of experiments in mice and other animals and have decided that the data they gather are representative of a normal behaving animal, so one can only assume the case may be the same for the octopus.