Just speculating: maybe it's because the language has shifted to more intrinsic concepts, such as connections with singularities, integrable systems, and such.

@Noah Schweber: thank you for the comments. Re PA as a metatheory: now that you make me notice this, probably I was just confusing "theory" with "language": indeed for the sentence $True(\langle\varphi\rangle)\leftrightarrow\varphi$ to even be stated the language of the truth theory must be that of the object theory (plus the new truth predicate symbol). But if the setting is completely general, we only need the $\langle.\rangle$ to make a sentence of $T$ into a term of $T^*$ and apply $True(.)$ - the languages of T and T* may be completely arbitrary.

@Timothy Chow: maybe I don't have a definite philosophical position about this. I am just sure that I'm not a Platonist; but abstract entities must come from somewhere: for me they come from language.

@Timothy Chow: yes, I guess so: at that level of the reduction, it's a matter of "philosophy of syntax" (if such a thing even exists) or belief based on sense-experience, not of mathematics.

"Strict formalist" - oh so that's the name of what I am. I think...

I'm wondering if the answers will get upvoted based on their pertinence/quality or based on the political views of the users making the upvote

Just a comment to ask a clarification about terminology. I think there are two senses in which the expression "metamathematical question" is used, namely: 1) a non-formalized philosophical question concerning mathematics; and 2) a question in a specific formalized metatheory [in particular, "metamathematical" in sense 2) is a particular case of "mathematical"] E.g. Goedel's incompleteness theorems are (mathematical theorems which are) metamathematical in the sense 2). Do I understand it correctly that you are using "metamathematical" in the sense 1) i.e. as a synonym with "philosophical" etc?