The depressing thing about the Einstein-Bergson debate is that they were both addressing a common problem from different angles that were not only compatible but in fact complementary.
For both of them, an idea of time that was just a function acting unilaterally on a passive backdrop of spcae was completely wrong. Both of them therefore sought to look past NEwtonian pretenses and show that extension is fundamentally a product of differences in motion.
But since Einstein's goal was to advance physics, his job was to improve the efficacy of a mathematically distilled idea of motion and extension where objects are distinguished a-priori and movement is the change in relative position between two objects. This is not a flaw.
I am not suggesting that he was working with, let alone creating, a procrustean bed; just that his job was to demonstrate certain invariants that hold across space and time in which one doesn't have to worry about anything more than the position/mass/acceleration of simplified bodies.
And of course what he showed was that regardless of what else happens, something's speed is relative to the speed of everything else around it with the exception of light (which always goes a constant 186,000 MPH), and that this dictates how moving faster in fact slows down chronological time.
But this is simply stuff that holds regardless of other changes in all the things omitted by physics. The spacetime of physics is a forgetful functor: it maps my path to positions and changes in position, it does not carry over other qualitative changes that may have transpired.
And this was Bergson's point about "philosophical time". Einstein says if you take two people and make one go much faster, he'll age slower than the other person, and all Bergson is saying is that in the real world (rather than the simplified world of a few variables), something else has to acount for why that other person started going faster.
But both of them are in agreement that extension does not exist separately from time, Bergson is simply saying that a truly encompassing idea of time must take into account all change and that relativity is true but it simply articulates relationships between a few attributes.
Anyone who says "but it's all just movements of atoms anyway so this is facile" ought to be laughed out of the room for missing the point: to suggest that is to once again presuppose a naive idea of extension a-priori and then layer time on top of it (supposing atoms with state, then defining time as nothing more than a mere change in such a state, therefore making time into something conceptually subordinate), the very pretense Einstein himself was challenging!
Nothing about Bergson's concept of "duration" contradicts anything relativity tells us, it simply defines a topological notion by which the future and the past are connected by a neighborhood that acts as a passage rather than existing as some isolated frame in a video.
Macro-scale physics does not and should not include this because such a thing is for all intents and purposes irrelevant to the relationships between force, mass, acceleration, and chronological time; but again these are relationships between a few distilled properties, not an exhaustive ontology.
And yes, calculus alone is enough to solve Zeno's paradox of the arrow, but that's because that paradox is about the basic kind of motion that classical physics is concerned with. Questions of how there's something "more" than mechanistic bumbling requires a different vocabulary.
And the importance of this is not just "what if we're like uh, nothing but stardust, man." It has serious scientific implications: without a mroe fitting ontology, we will be left in the dark on all kinds of practical questions where physics as we know it would just lead to an intractable N-body problem.
Every ethical decision has a texture that's inseparable from our instincts and their significance within a larger ecology, a dimensionality not capturable by "utility" (which is only an axiom enfocing transitivity within a model, not some a-priori idea of "value".)
Before anyone takes me out of context, this is not an injunction against the application of reason, it's a warning not to limit the application of reason to a tinkertoy approximation of reality.
Duration completely elides the dualism of Descartes and the epiphenomenalism of Berkeley by saying that life itself and the experience of qualities are defined by a process which grabs past and future in order to actionably bridge them together, or more fundamentally, that extension happens on account of this contraction that pulls past and future together, an idea complimentary to Einstein's own conviction that space and time are in fact not orthogonal.
And the reason why macro-scale physics can use an idea of time based off the technology of clocks is because it (for good reason) ignores these actions, as it only cares about what holds necessarily between certain basic forces. Duration, by contrast, is about what past and future are in relation to a subject that pragmatically utilizes them in any way it sees fit.