I think you are going down the route of "will they be a hive mind", whereas I am going down the route of "the definition of what it means to be 'you' will have to change. You say "Also, it absolutely does not imply that only the original can enjoy the memories, they all have them (as you accurately write), so they all will enjoy them." but if everyone has the same memories, aren't they all the original enjoying the memories? The concept of "original" only applies out here from our discussion. Inside the scenario there is no meaningful distinction between original and not.

If "you" are "the original" then stepping into the teletransporter and being disassembled killed "you". "you" died. If "you" are the clone, then stepping into the teletransporter moved you. You didn't die. If the original and the clone both walk out of the machine, the single lifeline branches into two, and English and law and conversation don't have common words to describe what happens next.

To me the problem is not "do the two people telepathically have the same thoughts", the problem is that from the viewpoint of the original I walk into a teleporter and walk out of it. Someone on Mars alledgedly exists but I have no knowledge of their experience so they can't be me. From the viewpoint of the clone, I walk into the transporter and arrive on Mars. Someone on Earth alledgedly still exists but I have no experience of it so they can't be me. I set out to travel to Mars, arrived, and so I clearly am the original. Both situations are individually coherent, but they shatter my expectation that "I" will have a single future.

Both people think they are the original. In the case of this hypothetical, the clone is identical in every way so even God pretends not to be able to tell the difference.

It's language, society, law, convenition which breaks down. Which one gets to sleep with nautilus' partner? Does the partner have any reason to prefer one or the other? Does the partner have any right to accept one nautilus and spurn the others? If the transported are different people then a marriage contract applies only to the original. If they are all the original and all the same person, what happens.

To me it is an argument about word definition, and about subjective experience, not about spooky action at a distance and soul transference.

My personal conclusion is that I need to set my thoughts up pre-branching so that I would be equally happy to walk out of the transporter on Earth or on Mars, because I will do both. See also stories by Greg Egan exploring this theme, like the guy who was mind-uploading himself into a computer, but his thought process was always that the person outside was "really him" and so when he woke up inside the simulation he was bitter that he was an inferior copy and the original was "free" outside. Or the one where the characters had a machine (jewel or dual) implanted into their skulls at birth which cloned their brain patterns into itself as they grew up, then the brain was removed and the jewel carried on so they could be immortal. People who always identified as the meat brain felt like brain removal was death and an imposter was taking over. People who identified as the dual, merely "learning" from the meat brain felt like it was no problem. From the outside, nothing measurably changed before/after the removal of the meat brain.