Are the paths in a Feynman path integral not observable?

In order to observe a specific path one needs to design an appropriate observable. Clear discussions on this subject are usually appear in the context of the two-slit experiment, although it is not the first thing that comes to mind when one is dwelling on all the mathematical difficulties of the path integrals. Some specific realizations of the two-slit experiment are even explicitly called "Which path interferometer".

Another important aspect of this question is how mathematical formalism and physical reality are not the same. Path integrals and Feynmann-Dyson expansion produce the same results for the observables, but the intermediate mathematical steps may significantly differ and do not necessarily correspond to anything real - they are just human-invented tools for getting the correct answers.