So it's like the same algorithm operating on different data?

To be clear, just the part about feeling like I'm "me". I think it would feel very different to be an alien, but I expect I would feel the same way about being myself.

On some level of abstraction this is both trivial and meaningless: at the bottom we all are just "particles following the same laws of physics"

I agree about the triviality. Especially for the thesis that we all share one consciousness -- that we are all a physical computation is both obvious and meaningless (everything is a physical computation) but it also means it doesn't matter if that particular computation is displaced in space or time or copied -- there's nothing unique that doesn't get carried over (if it's true that all our senses of self are essentially the same computation).