You're making a familiar category error here.
The methods you are talking about all correspond to some logical or algebraic structure or other, which is 'just math'. Similarly, they each have a particular implementation, which we might describe as 'just programming'. Neither math nor programming are well described as Frequentist, Bayesian, or anything like that.
Put another way, the same mathematical structure can be Frequentist, Bayesian, some third thing, or a mix depending on how its elements are used for inference (which is something you do, not something the model has or does).
OLS is an algorithm (minimize the sum of squared errors) and can be motivated as a Frequentist method when it is chosen for the behavior of its output in repeated samples, or a Bayesian tool for getting a key parameter of the posterior distribution under certain assumptions about the prior distribution of parameters, or as neither when it is motivated as an interesting application of singular value decomposition, or some other linear algebraic tool.
Brown, Cai and Dasgupta, 2001 show that a Jeffrey's prior on a binomial proportion - something at least notionally Bayesian - behaves very well in repeated samples, and can be justified in a Frequentist way (Section 4.3), that is, in a way that makes no mention of beliefs about the value of the parameter.
Think about dessert wines. A dessert wine is a wine that typically drunk with dessert, not a wine made in a special way or from a special kind of grape. It's true that dessert wines tend to have some characteristic properties, e.g. they're sweeter, but those features are not what makes them dessert wines; that's the dessert.