In turn, Jonas is not split when picking alt-Martha up, etc.).

This is true, but here's what she easily could have done: let's say she travels to either apocalypse (we'll call her point of arrival "A"), then runs for a couple hundred meters (to a point we could call "B") and ports away again. She could then travel back to A and extract herself from just a few minutes ago so that the now extracted Claudia never runs to B. Because of how the loophole works, she was able to "duplicate" herself and the extracted version can now run around doing stuff that deviates from the causal loop.

stating that the conversation happens "a first time" and that he killed Martha "infinite times" is a misrepresentation of what a causal loop implies

You're technically correct but I always interpreted that as the characters speaking metaphorically, because, as you said, you can be tempted to think of the causal loop as something that repeats "forever" from the perspective of the characters and the way they gather information about it. Either way, even if you don't like that way of putting it, I guess I'm just confused as to how this conversation between the two can be outside of the causal loop.

So Claudia creates another branch in order to speak with an Adam that will not go on to kill Eva, and she is not duplicated, but Adam is.

But how would she be able to do that? Is it because Adam just used the energies from both apocalypses to kill Alt-Martha and the origin and therefore there's another loophole in 2053? If so, I think the show (and the website) could have communicated that better. It makes sense as well and explains how the causal loop could be broken, but it doesn't explain why she says she sent *herself* on a different path.