By far the most widely-used calculational framework in standard QM is the algebraic matrix mechanics approach, pioneered by Heisbenberg, Dirac, Hilbert, von Neumann and others in the mid 1920s. It involves state vector representations of the state of a system, encoded via complex-valued vectors representing probability amplitudes (i.e., a Hilbert space). This state vector is a specific way of encoding the configuration space of the entire set of relevant variables, and is thus manifestly non-local, and represents the entire state a given point in time, in a way that is thus incompatible with the principles of relativity.
This state vector evolves under unitary transformations (rotations in the complex vector space), which preserve the overall magnitudes of the vectors, even as they rotate around in the space. The unitary nature of the rotation transformations represents the behavior of the system when it is being governed by the Schrodinger wave dynamics under the Copenhagen dualistic framework, which perfectly preserves the overall underlying probability space as long as nobody “looks at it the wrong way” (i.e., makes a measurement). Then, at the end, a “measurement” is made by collapsing the probability space down to a single discrete outcome (i.e., along an eigenvector of the resulting state).
This matrix formalism is equivalent to a self-consistent form of probability theory, which can be derived from abstract axioms having nothing to do with quantum physics (Gleason, 1975; Jaynes, 1990; Caves et al., 2002; Fuchs et al., 2014; Mermin, 2018). Indeed, this framework is so general that its only real physical commitment is that quantum physics obeys strict conservation laws: if you start with X amount of spin distributed however uncertainly across some state variables, then you have to end up with the same total uncertainty in spin distribution at the end, prior to the final measurement step, when everything collapses.
Thus, the claim that standard QM is such a successful framework must be understood within this context: yes, it is accurate in capturing this basic fact of conservation, but it really isn’t going very far out on a limb here: nothing wagered, nothing lost; but also perhaps not so much gained.