None of these examples are of theories like our current hot Big Bang model getting ruled out by observation, with no better theory replacing them, which is what the post I was responding to claimed can happen.
The first, in fact, is not even finalized yet, because there are still unresolved issues about the actual value of the Hubble constant: different sets of observations point at different values and the discrepancy is not fully understood. (Google "Hubble Tension" for much more.) But this whole general line of research is not about "ruling out" a theory, and it's certainly not about putting some better theory in its place; it's about refining our existing theoretical model by adding more and more reasonably confirmed detail about the actual distribution of matter and energy in the universe and its actual expansion history.
The second is a particular kind of hypothetical particle that has never been observed, still never having been observed. That doesn't "rule out" the existence of that kind of particle with 100% certainty. It just means we still haven't observed it. (Even the article you reference notes that there are still axion models that have not been ruled out.) And it doesn't change our best current model of the universe at all.
The third "rules out" a class of models that nobody has ever used. Similarly, the fourth "rules out" a model that was not even built to be used, but was expected to be ruled out, at least at the level of accuracy of these particular measurements. (That accuracy, as I understand it, is still well short of the Planck scale, which is where most physicists expect any "quantization" of spacetime itself to show up.) These results are useful in that they narrow the space of possible models that scientists might consider trying to use in the future; but they bear no resemblance whatever to what Eric Lerner claims (incorrectly, in my view) is shown by the James Webb telescope observations, which he claims "rule out" the entire Big Bang model.