> Of course, he doesn't actually give a concrete answer, but he very strongly implies that the question has an answer, i.e. that the question is a meaningful one to ask, and that implies that the MWI does in fact mean that there is a discrete number of clearly separated worlds.
In the video, Sean Carroll talks to a non-expert audience, so he must simplify some things, and then it is your or my guess about what the unsimplified version was supposed to be. He says something like: "we don't know, even whether it is finite or infinite, but if it is finite it is a very large number such as 10^10^123". But notice that he also uses as an analogy an interval from 0 to 1, which can be split to half as many times as you need.
You see this as him believing in discrete separated universes, of which there is a definite number (potentially infinite). Yes, that makes sense.
I see another possible understanding, that he is talking about "meaningfully different" universes, because that is what we care about on the macro level. To explain what I mean, imagine that we observe two particles. Any of them can be in a huge number of possible positions, moving in a huge number of possible directions, at a huge number of possible speed. But if we ask whether those two particles hit each other and transformed into another particle, that kinda collapses this huge possibility space into a "yes / no" question. Out of practically infinity, two meaningfully different options.
On a macro level, either the cat is alive or it is dead. Those are two meaningfully different states. If we focus on one particle in the cat's body, there is a continuum of where precisely that particle could be, and what momentum it has. So from the particle's perspective, there is a continuum of options. But from the cat's perspective, and the cat's owner's perspective, this continuum does not matter; unless it changes the macro state, i.e. the particle kills the cat, or at least maybe hits its neuron and makes it do something differently. So it seems possible to me that Sean Carroll talks about the number of worlds that are different from human perspective.
Then there is another problem in physics that we don't know how/whether the very space and time are quantized. We use the mathematical abstraction of a "real number" that has an infinite number of digits after the decimal dot, but of course that infinite number of digits can never be observed experimentally. We don't know. Maybe it is something like what Wolfram says, that on a deep level, spacetime is a discrete graph evolving according to some rules. If something like that would be the case, that would reduce the possible number of states in the universe, even on the micro level, to a huge but finite number. And the mixed state of the multiverse would consist of this finite number of branches, each of them assigned a tiny complex amplitude. So that's another way how things could get finite.
And I am saying this just as a random guy who never studied these things, I just sometimes read something on the topic, and some ideas feel to me like obvious consequences of the stuff that is "in the water supply". So I believe that if I see a solution to a problem, then if it makes sense, someone like Sean Carroll is 10000x more likely to notice the problem and the solution, and develop it much further than I ever could. Or when you make a survey, and a half or a third of people who study quantum physics for living say that some version of MWI seems like the correct interpretation to them, I don't believe there is a simple devastating argument against it that all of these people have simply missed.