Around 2020, I decided to try to learn as much as I could about "higher" mathematics in earnest, having basically no background in the subject. Five years later, I have finally read and suffered enough to be able to pick up texts in any of the abstract branches of mathematics and at least understand most of what's being shown/said at a basic level.
More fascinating to me, though, is that this shift in focus has lead to a definite shift in my thinking. My thinking used to be almost hyperlinguistic. Words were my medium of choice, and I had a strong stream of inner linguistic thought running through my head. Now, that inner voice is mostly quiet. I also find that I tend to think about certain situations in terms of abstract "relationship pictures" rather than a descriptive sentence.
I actually kind of miss the old linguistic tendencies I had at times. I'm hoping a shift back into literature helps reestablish some of that.
And yeah, as with all general proclamations that sound nice because they allow us to seemingly boil complexities down to a singular thing, the whole "wiring is thinking" idea isn't true. The truth in that statement is more akin to "human thought is often tool assisted"—and a manner of tools can aid in elaborating thought. Thought and action are not as severed as we tend to think.