In many ways Einstein's reception of empiricist and Kantian ideas (mainly through Mach and Poincaré) shaped subsequent theory building in physics, and as a result philosophizing about science in positivism and in post-positivism. Relativity as "the last classical theory" is a modern anachronism with a benefit of hindsight and relative privation to later issues in quantum mechanics. Lorentz, Poincaré, etc., saw it differently at the time.
In philosophy specifically, Einstein's contributions were to fully expose the unphysical character of Newton's absolute space (and ether as its reification), and later of space, spacetime and spacetime points in general, clarify Mach's vague ideas about its relational nature and derive consequences of that for physical theories (general covariance), but to reject Mach's and Poincaré's fictionalism and conventionalism about physics and geometry overall. In this he acted as an heir to science oriented Kantian creed of Helmholtz and neo-Kantians. The latter and logical positivists, especially Cassirer and Reichenbach, made changes to the doctrines of space, time, and empirical knowledge more broadly, specifically to account for changes introduced by relativity.
Cassirer's Substance and Function And Einstein's Theory of Relativity (1910/21) was one of the first assimilations of relativity by a major philosopher. Based on it, Cassirer rejected Kant's characterization of space and time as forms of pure sensibility, and described them instead as initial forms of conceptualization by understanding, which can be refined by advancing science into more elaborate forms, such as Einstein's spacetime. Reichenbach in Theory of Relativity and A Priori Knowledge (1920) takes the logical structure of general relativity as a logical blueprint for general empirical theories. He distinguishes "axioms of connection", laws connecting experimentally accessible empirical concepts, and "axioms of coordination", non-empirical principles required to make concepts empirically meaningful in the first place. Without the axioms of coordination, such as the constancy of the speed of light, and the equivalence principle in relativity, the concepts like inertial frames or energy have no empirical meaning, i.e. spacetime and the metric tensor are presupposed a priori.
This Kantian fusion was directly inspired by Einstein's musings about the role clocks, rulers, masses, etc., played in interpreting relativity physically. According to Friedman, "in Carnap's Logical Syntax of Language we find a revival of the relativized a priori in something very like Reichenbach’s original sense". Carnap saw Kuhnian paradigms as a historicized version of his linguistic frameworks. Friedman himself takes Reichenbach’s distillation of Einstein's blueprint, along with Cassirer's framework, as starting points for encapsulating Quinean and Kuhnian relativism into a multiscale hierarchical model of evolving scientific knowledge, see e.g. his Einstein, Kant, and the Relativized A Priori.