I think they are both true and closely related. Typically and colloquially, when people talk about meaning they are talking about some state of affairs about what is good or bad with respect to the universe (if the universe includes things like God, a world of forms, ideas of perfection, etc).

I think its very reasonable to believe that the universe does not have any of those properties and that life is random and has no inherent or universal meaning.

I guess there could be some kind of subjective meaning but I don't really see the utility of that idea.

In this particular case you would only have to push back the lack of meaning to the ~multiverse or whatever a sequence/family of child universes would be called.

I don't think Tegmark <IV had any simple parameters for goodness or meaning, and neither does logic or mathematics. We assemble our meanings out of more fundamental relationships but I actually think they concretely exist in a real way as real as the matter in this universe, but more in the way that galaxies and other complex structures exist. Meaning is a property of complex self-reflective systems and so inherent meaning will probably always be tied inexorably to context and environment, or in our case meaning is tied specifically to our human nature.

E.g. I will find it fascinating if universes do evolve from progenitor universes and therefore the guiding selection pressure is "make more black holes/universes" but that isn't the same thing as the human concept of "good" since our nature isn't aligned with entire (families of) universes.

But, speaking precisely, there is no human nature at all. You and I have nothing fundamentally in common except that our atoms happen to be organized in a similar way. We have no nature in common except as a coincidence.

It is a coincidence that delights me and I happen to feel quite a lot bonhomie for my fellow human beings and lifeforms, but I don't see how it makes life meaningful in any universal sense.

Do you consider the relationship of two molecules of water to be similarly coincidental or along a continuum from e.g. the nature of two elections all the way to how two universes might be similar? I figure fundamental particle nature is less coincidental than human nature, which is correspondingly less coincidentally related than two heterogenous dust clouds.

I don't see any reason to have a strong belief about why any fundamental constants are what they are. This is so far beyond what even our best physics can say anything meaningful about that I feel an obligation to studiously have no opinion about it.

I will say that I see no compelling reason to believe that the values of fundamental constants are NOT just random.