Frequentist inference with Dirac delta as prior Would likelihood-based frequentist inference amount to the same as Bayesian inference, but where the "frequentist prior" $\pi^F(\theta) = \delta_{\theta^*}(\theta)$ with $\delta_{\theta^*}$ being the Dirac distribution centered at $\theta^*$?

It is true that frequentist inference assumes that the parameter is a constant.
In terms of a prior function you could indeed imagine this as delta function.
But, the inference problem is that the parameter is unknown so we do not know which delta function to choose. And in terms of the interpretation of prior functions as expressing 'belief' instead of some actual population distribution, the prior would not be this delta function.
