I've also seen the Gamexplain analysis and can definitely see these levels being little test chambers with challenges.
This also sparked this little theory in my head: Perhaps we play an Octoling who tried to escape from Octo Canyon, but was killed along the way. Maybe not killed since that could be too dark for Nintendo, even with all the dark lore this series already has, but beaten down enough to where Agent 8 couldn't reach that goal. Sure, this would likely have to mean that the soldiers in the single player campaign are also brainwashed, but I think it could still work.
Cap'n Cuttlefish and Agent 3 would find Agent 8's corpse or weak body and cut off their tentacle to attempt to clone it. And Octorians are born by cutting off their tentacles. This could explain why you have no memories of your past and the test tube scene. You're a clone of yourself saved by Cuttlefish and Agent 3. It could potentially also explain why the announcer said you play an Octoling in a puzzled manner as pointed out by Gamexplain. There could've been something that they had to add to bring you back to life that doesn't quite make you 100% octoling. Maybe a little Inkling DNA had to be donated and made you slightly different. As someone, somewhere on the Internet pointed out, the ears look a little weird. They're different from each other. Plus, I thought the face looked slightly strange. Not in the ugly way but that it felt like it was off somehow. You're cloned and you wake up where Cap'n Cuttlefish has waited for you. He recruits you as Agent 8, and sends you off to these testing facilities in hopes that these will bring back memories of the soldier seeking freedom you once were. Agent 3 could be around to make sure that Agent 8 doesn't turn back to a soldier fighting Inklings or support Agent 8 in little ways. Such as weapon tips or hints of your past. You enter these chambers and you slowly regain your memory, learning that you were once against Inklings until you decided to flee. To run away from the hypno-shades and join the surface. As for the Squid Sisters earworm, I think there's one of two possibilities. You're a soldier from either the Octavio vs Agent 3 fight, or the Octavio vs Agent 4 fight. I think the one against Agent 3 is more likely. I agree with the people who think this takes place at the same time as Agent 4's story, and I believe this could help explain why Marina is around. Pearl probably knows her way around the subways like the back of her hand. She's probably taught Marina but if she already knows where to go why is Marina necessary? The sunken scrolls confirm that Marina was once an Octoling soldier in the crowds of the fight against Agent 3. She also might've helped save you along with Cuttlefish and Agent 3. She could've known you as a soldier in that crowd for all we know or could at least recognize you as one, and probably recognized your body before being cloned. Or Marina knows the potential struggles of an Octoling trying to escape from Octo Valley/Canyon. So even if she couldn't recognize who you were, she could tell you were one of the unlucky Octolings trying to escape but couldn't. She found your body first and brought Cap'n Cuttlefish and Agent 3 to you, to which they decided to let her and Pearl join their research mission.
So, you're cloned and you wake up with a familiar song you've never heard of stuck in your head. That being your only clue to your past. A strange man is waiting for you and take you to the subway. There's an octoling there who looks like someone you've seen before. Suddenly, you're pushed into a testing facility, the first of many. Slowly they bring back a memory, and then another memory, and another, and another until it becomes clear. You're one of the soldiers who you've been running away from this whole time along with the same octoling on the subway in a crowd watching something. There's some sort of large machine fighting an inkling, the same one you now recognize as someone who's helped you regain your memory. In the distance the strange old man is dancing in rags. During all of this, a song is playing. The same song as when you first woke up.
Sorry for the long and jumbled up mess but when I think of these I may or may not put too much detail into them. Feel free to comment on this, positive or negative.