Maybe he didn't overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn't very good evidence in itself, compared to relatively naive considerations like "using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as 'real' as our world doesn't seem likely to hold water".

I place less value on metaphisical intuitions about what 'real' means. I do not particularly like the baggage that comes with MWI, I do like the principle of asserting that we can consider reality as we understand it to be more or less just like the core math - with any additional mechanisms required to make our intuitions fit rejected out of hand.

The undesirable baggage of "MWI" extends to the titular concept. The whole idea of "Many Worlds" seems to be a description that would be made by those stuck in the mindset of someone stuck with trying to force reality to be like our metaphisical intuitions of a simple classical world. As far as I am aware experiments have not identified any level at which the worlds are discrete like that (except for the sense in which you could allocate each possible configuration of a universe down to the level of plank distances and suchforth as a 'World'.) So the question "are the other Worlds 'real'" doesn't seem to qualify for a yes or no answer so much as a "huh? There's just a 'reality' of the stuff in this wave equation. Call some specific subset of that a 'world' if you really want to."

It's been two years since I read the QM sequence.

It's been at least that for me too (it isn't a sequence that works in audio format, which is my preferred media). I place very low confidence on what I remember of QM from there and research elsewhere and only placed slightly higher confidence on my understanding even back when I remembered it.

There are certain assertions that I am comfortable rejecting but the specific positive assertions I have little confidence. For example I have no qualms with dismissing "but they are all just 'interpretations' and all interpretations are equal" sentiments. If additional mechanisms are introduced that isn't just interpretation. Interpretation is a question of which words are used to describe the math.