I wrote a review of this book with chapters by Penrose, Witten, Connes, Atiyah, Smolin and others:
• John Baez, review of Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, edited by Joseph Kouneiher, Notices of the American Mathematical Society 66 no. 11 (November 2019), 1690–1692.
It gave me a chance to say a bit—just a tiny bit—about the current state of fundamental physics and the foundations of mathematics.
Azimuth 
Penrose has a fairly recent book I saw (and borrowed) from the library—i think its ‘road to reality’ (2016) . Max Tegmark also had one in there—Penrose’s book i viewed as of much higher quality—less popularization, and more math. (I disagree with Penrose over a few things he wrote about ‘consciousness’ , but his background is not in biology). .
I wonder if you have come across the ‘Vaxjo interpretation of quantum mechanics’ from Sweden.
Smolin had some interesting popular books—i can’t say i understand this—along with Julian Barbour, C Rovelli, etc. (I’m more interested in Ricci flow and its connection to classical diffusion problems– or even the ‘classic paper’ by Marc Kac ‘can you hear the shape of a drum?”.
I also ‘wonder why i wonder why i wonder.. ‘ about any of this. i guess it passes the time.
I’m not really interested in popular physics books these days.
Penrose’s Road to Reality would have been absolutely wonderful to read when I was student. It would have saved me years of work, because he explains a lot of mathematics and physics in a detailed yet friendly way. As you suggest, it’s not popularization so much as clear explanation.
I like your book review (though much it is above me).
Not to clutter your list i’ll just say for completeness, https://arxiv.org/abs/1210.2390 describes the ‘Vaxjo interpretation’ .
(I think its closer to E Nelson’s Stochastic Dynamics or Bohm’s ‘quantum potential,and ‘stochastic electrodynamics’ (largely discredited, but even people at MIT still study some aspects of that..)
T’Hooft was advised to go into physics by N G Van Kampen—a relative–famous in statistical mechanics , and one of few people i thought i could understand .)
.
Category theory came up recently in an ‘ecology’ list I’m on and it mentioned your page and its references—but the people on that list were mostly interested in applications to programming (eg Haskell–i’m not a programmer). .
Most pop science books i have seen recently seem to mostly rewrite things that have been written in pop books many times before. (Penrose is an exception.) (My favorite pop math book was by Tobias Dantzig –‘number: the language of science’ –my father got that in a used book store for 50 cents. His son is known for linear programming, and i see that as related to ‘potential theory’, calculus of variations, multiobjective optimization and even diffusion and ricci flow.)
(Last paper i read by L Smolin was on ‘gauge theory of economics’ (on arxiv) —it seemed to be either correct or on the right track (and seemed to rephrase the SMD theorem of economics in physics terms–S is Sonnenchein who became president of U Chicago; M is Mantel and D is Debreu. )
.
I have one of the earlier editions/printings of The Road to Reality. It probably holds the record for the most typos I’ve found in an otherwise serious book. I understand that there is now a website dedicated to those typos.