Let me clarify, again, the old misunderstanding, by pointing out that licences don't inhere in code, their obligations attach to recipients through the act of conveyance.
If you are the sole rightsholder in some code, and you release it under some non-AI (and thus non-free) licence, and you also release it under AGPLv3, those recipients that receive it under AGPLv3 are completely unaffected by any restrictions that applied to those who received it under, say, Apache2-nonAI. Conversely, those who received it under Apache2-nonAI are completely unaffected by the requirements of AGPLv3.
So hopefully that deals with your second question, "If I publish my work under AGPL-3.0, could those licenses interfere with my current license?". No, they couldn't.
As for the larger question of how to prevent your code from being used for machine training, well, the licences you list should achieve that, but at the expense of making your code non-free when so licensed (and given a solution to the detection-and-enforcement problem, which is non-trivial). The larger question of whether the output of an LLM is a copyright derivative of its training inputs is still very much a live legal question, and I don't think anyone knows how the chips are going to come down. If it is eventually decided the output is a derivative of the inputs, that will completely torpedo proprietary LLMs, as it's a rare one that won't have scooped up some copyleft-licensed inputs in its training maw.
I personally think the problem's going to go away fairly soon anyway, as the internet fills up with the output of trained machine models which is then used in turn as training input for the next generation of machine models. There is some very interesting work from the University of Cambridge showing that "using model-generated content in training causes irreversible defects", and that within a few generations the outputs become indistinguishable from garbage (and they're clear the work is not limited to natural language models, or even to text-based models). Since there is no generally-reliable way to distinguish model-generated content from human-generated content (see many long discussions here on meta.SE) I don't see how this effect can be long avoided, and the whole problem will disappear up its own tail.