Are these titles then the wrong avenue for learning math?
Projective Geometric Algebra: Illuminated (2024) (Not mentioned directly in the article [1]; including a quote from link [2].)
Algebraic Calculus (2016)
Divine Proportions: Rational Trigonometry to Universal Geometry (2005)
[1] https://terathon.com/blog/poor-foundations-ga.html
[2] "If you want solid foundations, this book is for you."
Math professor here. If you want to learn math, then for the most part I recommend choosing time-tested avenues, using popular materials.
There are two reasons for this:
(1) Popular materials are usually popular for a reason: they reflect an approximate consensus, across a significant fraction of the mathematical community, that their approaches are more-or-less the best.
(2) If you learn the same way everyone else does, you'll have an easier time talking to others and finding materials on the internet.
I know some very innovative books which I highly recommend, for example Visual Group Theory by Nathan Carter:
https://bookstore.ams.org/clrm-32/
But the innovation is pedagogical, in what Carter chooses to emphasize and how he presents everything. At the book's core, Carter agrees with everyone else about what the foundations of group theory are and should be.
Even Sheldon Axler's Linear Algebra Done Right (another excellent book), with its hilariously provocative title, only differs in its choice of emphasis and order of presentation. His choices are quite compatible with everyone else's.
https://linear.axler.net/LADR4e.pdf
Rational trigonometry is useful in some contexts (I’ve optimized trig computations with it in the past) but I wouldn’t call it GA, it’s a different kind of beast.