In the folk parlance of statistics, OLS tends to be identified as a frequentist approach to parameter estimation because it does not explicitly involve a prior distribution on the parameters being estimated. But strictly speaking, OLS is just a mathematical operation whose result has both frequentist and Bayesian interpretations.
From a frequentist perspective, if the usual linear model assumptions hold, the OLS parameter estimates are equal to the true parameter values plus an error of known distribution derived from the randomness of sampling. This enables us to extract information about the estimates (e.g. p-values and confidence intervals) which have theoretical guarantees that limit the chance of certain types of errors attributable to random sample variation.
From a Bayesian perspective, if the usual linear model assumptions hold, OLS provides the maximum a posteriori (MAP) parameter estimate under a uniform prior. The posterior distribution is a multivariate Gaussian with a peak at the MAP estimate, and we can use the posterior to update our prior on the parameters, or compute credible intervals if we so desire.
In general, the frequentist/Bayesian distinction is fraught with so much folk connotation and association that most statistical methods end up feeling like one or the other to practitioners. But at bottom, if this distinction has any objective meaning, it is about how you interpret probabilities, and your choice of parameter estimation method does not necessarily say anything about how you interpret probabilities. Only your interpretation of the parameter estimates can identify what side of the distinction you are (currently) working in.