Interesting. The vocabulary disconnect with General Relativity (which is the more relevant theory of relativity here, I think) is pretty frustrating, although one thing that struck me is that at the time Bergson was making these arguments, there was a lot of GR jargon yet to be invented. Also, crucially, a formal process for foliating a "block universe" spacetime was decades off (the 3+1 Arnowitt-Deser-Misner formalism arose in the late 1950s), so a late 1910s criticism of GR as treating the timelike axis as "dead" like the spacelike ones was almost reasonable.

Other important and relevant tools were either extremely fresh (e.g. Noether's first theorem) or had yet to be formalized (e.g. gauge theory), and these put practical limits on conceptual attacks on dynamical spacetimes (that's one reason why externally static vacuum metrics, like Schwarzchild's, were popular at the time). Numerical relativity wasn't even a dream in the 1920s.

However, in spite of not-yet-existing tools, it was pretty clear that General Relativity's coordinate freedom combined with diffeomorphism-invariant models of matter would accomodate standard approaches to time-series evolutions of field content (e.g., initial values surfaces and physical laws). Additionally, "ticking clocks" that appeared in Einstein's and others' GR papers were meant as shorthand for much more general objects -- basically anything that has some state that isn't time-translation-invariant. Ideal gases and other thermodynamic composite "objects" count, as do fundamental particles, as does an entire expanding or contracting universe. "Ticking" is simply the application of some arbitrary coordinates (not necessarily linear or even uniform ones; in GR they only have to admit a diffeomorphism) on those "clocks".

One of the interesting things that was pretty fresh prior to Einstein's Nobel was the resolution of the hole argument, which essentially abandoned manifold substantialism. Spacetime without a clock is simply an irrelevance; it's only the presence of at least one (or more) "ticking clocks" that gives meaning to any system of coordinates one puts down on the manifold -- and in particular it's the "ticking clock" or clocks that generate the metric; it is not something that is a property of wholly empty space, and that in turn led to a deeper understanding of the G_{\mu\nu} + \Lambda g_{\mu\nu} side of the Einstein Field Equations (i.e. the curvature of spacetime determined by the metric).

There was undoubtedly some "philosophy" going on in the early days of General Relativity, but frankly most of the work was on modelling gravitational collapse in general, which was both fairly difficult technically and also a deep well of unexpected consequences that were even more strikingly different from Newtonian gravitation than the Kepler problem in GR.

I'm fairly confident that the ideas raised related to this Bergson-Einstein debate were uninteresting (and possibly even mostly unknown) to most of the scientists exploring the golden age of General Relativity (1960s & 1970s mainly). GR, especially post-Einstein, racked up some extremely precise quantitative predictions of the behaviour of large bodies (and small things near large bodies) that matched later observations with high precision.

By the 1980s, the space for thinking about the philosophy of General Relativity was already mainly at inaccessible energy-densities or at almost pointlessly timelike-separations from us (e.g. the earliest we could see the consequences of black hole evaporation is about a hundred billion years in the future), so what's more interesting (I think) is the study of the mechanisms that generate the metric and the exploration of non-exact solutions, rather than picking at the scabs of GR's unremovable background.