we now know that it's possible to change the timeline in the few seconds during the apocalypse
We don't really know the timeline can be "changed", we only know it is possible to split the timeline into two different versions of events at the apocalypse, but that split could itself be part of the unchanging 4D structure of interacting timelines that is "the knot".
For example, at the apocalypse in the Adam timeline, alt-Martha was on her way to rescue Jonas, and the timeline split when alt-Bartosz either did or didn't appear. In the branch where he didn't appear, alt-Martha went on to rescue Jonas and then drop him in her own past in the Eva timeline--call this version alt-Martha 1. In the branch where alt-Bartosz did appear, he convinced her to go with him instead of rescuing Jonas--call this second version of her alt-Martha 2. But the key thing to note is that both alt-Martha 1 and alt-Martha 2 became integrated into the same Eva timeline after jumping away from the apocalypse in Adam's world, and in fact, the actions of both of them were already a part of alt-Martha's past before she split in two.
Consider the moment she was on the bicycle with alt-Bartosz, and then the older Magnus and Franziska appeared and told her to come with them so she could rescue Jonas--this was clearly before the split occurred. And yet at this moment she was already pregnant with Jonas' child, from the version of Jonas who had gone with alt-Martha 1 and been dropped off in the cave of the Eva timeline. So clearly the actions of alt-Martha 1 were already a part of her past when she was on that bicycle ride. Meanwhile, alt-Martha 2 was the one who shot that version of Jonas, and at the time of her bicycle ride with alt-Bartosz, the pre-split alt-Martha had already seen that happen (she cut her hair after she found she couldn't get the dried blood out).
So, this seems to establish that at least in some cases, if the timeline branches in two due to the apocalypse loophole and time travelers from either branch jump away from the apocalypse era, their later history after the split may be part of the seemingly fixed structure of the timeline, as opposed to changing it. This could be the case with Claudia as well. I think she was able to use the loophole by jumping to the time in 2053 where Adam was channeling the energy of the apocalypses in both worlds to destroy alt-Martha 1 (he had said that his machine 'focuses the energy of both apocalypses on this one point, concentrated')--in her dialogue with Adam Claudia specifically says she used "it" (the loophole) to make herself "run in a different direction" (which I interpret to mean sending herself into an alternate version of events different from the one in the 'main' timeline where Adam went off to kill Eva after her failed experiment). Here's what she said about 20 minutes into episode 8:
"I know where the loophole you’ve searched for all these years is. Time. During the apocalypse it stood still for a fraction of a second at that point and that threw everything out of balance. But when time stands still, it also momentarily breaks the chain of cause and effect. [Adam asks: ‘One can…change things?’] Eve knows that. She uses the loophole in your world to send her younger self off in one direction or another, and in doing so maintains the cycle. I used it to make myself run in a different direction too, to be here today. You must use it to send Jonas on a different path."
If she made use of the loophole by traveling to a moment where time was standing still due to the apocalypse energies, then just as alt-Bartosz was not himself duplicated in the last example, Claudia probably wouldn't be duplicated here. There would be one branch where she appeared to talk to Adam, and another branch where she just didn't appear, and the version of Adam from that branch apparently went off and shot Eva. In the first branch where she did appear, after talking to him and jumping away, she could go on to become the very same Claudia that we saw in 1954 in season 2.
I think there is some circumstantial evidence that the Claudia who talks to Adam is the same as the Claudia of season 2. After her talk with Adam, Claudia has a talk with her younger self (starting about 26 and a half minutes into episode 8 of season 3), where before she goes her younger self says "Dad. Tell him that I'm sorry." And in episode 3 of season 2 (about 35 minutes in), we had seen Claudia go into Egon's office in 1954 and apologize to him, saying "I want you to know that I'm incredibly sorry that things happened the way they happened. ... I truly am sorry."
Then later in that episode, about 48 minutes in, Claudia had her meeting with Noah where she was shot (something she knew was due to happen that night, as she shared a newspaper clipping about it with Agnes earlier), but she seemed oddly assured that everything was going according to plan, saying "I know that I am going to die. But am I going to lose this match? Or is this here, our meeting, you and your gun, only part of a game you still don't know how to play." So that would also fit with the idea that she had already sent Adam on his way to give Jonas and alt-Martha the plan to return to the origin world and finally undo the knot.
Also, if you go the section on Claudia on the official Dark website and swipe through the sequence of events in her life (illustrated on an evolving timeline), it indicates that the scenes with old Claudia in season 1 happened before her meeting with Adam in terms of her personal chronology, but the events of season 2 happened after that meeting from her perspective.
In any case we know that the last cycle was different from the previous one, because Eva remembers finding herself shot by Adam's hand, which doesn't happen.
That's not certain either, since Adam might have used the loophole to create another split, where in one branch he goes to talk to Eva but doesn't shoot her, and in another branch his alternate self who never talked to Claudia comes in (maybe at a later point in the day) and does shoot her. We know that some of these weird temporal energies can cross between universes, since 44 minutes into episode 9 of season 3, we see that Tannhaus' machine is shooting a beam of energy through the floor of the bunker in the origin timeline, and then Jonas and alt-Martha sitting in the tunnel of a different timeline see the beam coming through the roof. So, if Adam channeling the energy of both apocalypses to destroy alt-Martha in 2053 was what allowed Claudia to make use of the loophole at that date in the Adam timeline, it's possible the loophole could also be used on the same date in the 2053 of the Eva timeline.
So I think everything up to the moment Jonas and alt-Martha appear in the origin timeline can be viewed as part of a single self-consistent structure of interacting timelines where nothing within the structure is really "changed" (the scene in the tunnel of light where they were seen by themselves as children, and they could remember that from their own childhood, also suggests this). There's no onscreen evidence that Claudia had any proof of multiple "cycles" with different details, and in general we had seen in the past that characters seem to have faith in this idea despite the evidence available to them.
I also think this belief was something of a plot device to explain why characters would repeat actions they had already seen their older selves try and fail. For example, when the middle-aged Stranger Jonas tried to permanently destroy the cave passage at the end of season 1 but only succeeded at temporarily closing it, the younger Jonas knew he had failed, but in episode 8 of season 2 there's a scene about 6 minutes in where the younger Jonas is talking with Claudia about how he hopes he can make some little changes which allow him to succeed at destroying the tunnel when he gets to be that age. This might be plausible if he was thinking in terms of "cycles", but it wouldn't make sense if he was thinking in terms of a fixed 4D structure of events.