Bayesianism often seems to be regarded as a modern interpretation of probability theory, which displaced frequentism, but actually it was the way in which probability theory was always understood except for a short period in the first part of the C20th. I think it was well summarised by Maxwell:
“The actual science of logic is conversant at present only with things either certain,
impossible, or entirely doubtful, none of which (fortunately) we have to reason
on. Therefore the true logic for this world is the calculus of Probabilities,
which takes account of the magnitude of the probability which is, or ought to be,
in a reasonable man’s mind.” James Clerk Maxwell (ed. P. M. Harman), 1990, The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1, 1846-1862, p.197, Cambridge University Press
Frequentism is then seen as a particular way in which probabilities can be assigned in a reasonable man's mind. IOW Bayesianism and Frequentism are not opposing interpretations, but rather Bayesianism is a general interpretation and Frequentism amounts to a special case, which does have a great deal of practical application.
I would contrast this with so-called interpretations of quantum mechanics. These are just waffle. Even von Neumann's quantum logic is so mangled by Wikipedia that it has no bearing on what quantum logic actually is.
The predictions of quantum mechanics are not derived from interpretation, but from the mathematical structure defined by the Dirac–von Neumann axioms. Interpretations, by and large, consist of hand wavy arguments which bear very little relation to the axioms. In some cases, such as Bohmian mechanics, they ignore theorems following from the axioms (which prohibit determinism). In others, such as many worlds, they bear no relation to the axioms, and discuss things like "the wave function of the universe" which is a nonsensical concept in axiomatic quantum mechanics.
Many interpretations, particularly information theoretic interpretions, and interpretations like quantum Bayesianism, and Saul Youssef's "exotic probability theory" simply regurgitate in different words what was already said by Dirac and von Neumann, without adding anything of interest and usually without making direct reference to mathematical structure.
The exception is the orthodox, or Dirac–von Neumann interpretation, in which qm is understood as a mathematical structure for the calculation of probabilities of outcomes of measurement (either Bayesian or frequentist probability can be used). The difference in mathematical structure between this and classical probability theory is precisely that quantum mechanics does not admit hidden variables, whereas in classical probability theory it is often assumed that results are determined by unknowns. The reasons for this mathematical structure are the subject of theorems, not interpretation. I have written much more on this in my books (see profile) and in e.g. The Hilbert space of conditional clauses