(Saying this as someone who's read Kant twice and agrees with most of what he claimed. Outside his taste in music.)

I assume you mean the Critique of Pure Reason? Kant's Oeuvre is quite vast, though it wouldn't be unreasonable to have read the 3 critiques twice.

>What would Kant add to this discussion that the physicists in the article haven't considered?

Kant himself, I'm not sure, but its his model of the cosmos that we employ today, and spatio-temporality is a development out of his critical philosophy, especially his aesthetics. If you want to break space and time out of spatiotemporality it helps if you are familiar with the metaphysical undergirding of contemporary physics, since we have not treated them as separate since Einstein, even though Kant originally kept them as completely separate intuitions and did not seek to unify them but only to try and see what happens when they are set in relation. That is to say that spatiotemporality is, if we are being good Kantians, an entirely negative, transcendental view of space and time since it does not appear at the level of the senses but rather as an abstraction from them. But if we treat the second-level abstraction as real then we are bound to make errors about the empirical world, as returning to the critical project would, I believe, greatly help in re-evaluating our empirical methods.

To be clear, you're suggesting that physisticsts reject general relativity's unification of spacetime because Kant, who obviously had no knowledge of GR nor the empiricism that supports it, did not unify them? Kant's Prize essay also pre-dates e.g. Gödel. That doesn't mean every modern mathemetician must first consider a Kantian slant to their work before rejecting it for well-established and obvious reasons. (Nor that Gödel disproves Kant.)

Deducing that Kant would want us to reject modern science because it's not based on our senses ignores entirely his work as a mathemetician. Kant was, in his own time, a modernist. Not a proto flat earther.

I am suggesting that if someone wants to escape from the current paradigm of physics it may help to understand how it came about instead of wasting a lot of time speculating about what space and time “actually” mean.

And in any case, there is nothing in math that prevents someone from being a flat-earther. If nothing else, set theory and qauntam mechanics has done nothing but flatten our empirical world. Kant was Modern but his work was not, one can read his Opus Postumum as an attempt to reconcile his physics with an intuition that would be capable of bringing about the “feeling of life” that arrives from the experience of natural beauty—which, while very odd, clearly follows from the 3rd critique and the critical project more broadly, unless you throw out the concept of Freedom entirely and all the moral philosophy that follows from it and stay, as some have, in the analytic. But that’s clearly not what Einstein did, Einstein is a Schopenhaurian, he based GR heavily in the Aesthetic, but an Aesthetic devoid of this possible “third” intuition, that of feeling of form, since spatiotemporality annihilates all other possibilities of dimensionality besides space and time. Now what I’m saying is, its not possible for contemporary physicists to critically interrogate their theories without having a solid intellectual grounding in how they came about. Doesn’t mean that someone couldn’t simply come up with something new and brilliant spontaneously, but not by questioning spatiotemporality itself but by developing an entirely new framework that disregards it.

But that’s much more difficult than starting with the basics, right?