Yes, so maybe think twice before eating one.

> We also have a nervous system distributed throughout our bodies, so we do experience the full body, but the neural signals are sent to one location, not nine.

Mostly yes. But we do have some processing that bypasses the brain: reflexes for example. The classic example is the kick reflex that doctors test with a small mallet on your knee. Or when you blink as something flies towards your eyes. It happens and your brain gets informed afterwards.

But there are degrees of non-conscious processing, from the heart beating by itself and your guts doing their things, to the breath which will be on autopilot until you take control over it, to entirely voluntary things like moving about your limbs (for healthy individuals).

Maybe the octopuses experience their disconnected brains somewhere on that spectra, where the limbs are semi-autonomous unless it focuses on them? (All we can do is speculate, there is no known way to learn the qualia of being an octupus.)

Other Minds: The Octopus, the Sea, and the Deep Origins of Consciousness [excellent]

https://www.amazon.com/Other-Minds-Octopus-Origins-Conscious...

If you haven't read it, you might enjoy Adrian Tchaikovsky's Children of Time series. It's fiction which explores different intelligences, with the second novel[0] dealing specifically with octopuses.

[0] - https://en.wikipedia.org/wiki/Children_of_Ruin