Given that the “erratic mode” only impacts the beginning of the run and disappears suddenly at known locations, this sounds like an issue of delayed GPS lock.
And given that the problem didn’t exist in the past, it could be a software issue due to upgrades. Or it could be a hardware issue that developed over time, such as something impacting GPS receive sensitivity. Or it could even be a new source of RF interference in the GPS range near the author’s start point, which impacts GPS lock until they get far enough away from it.
Interesting issue, but note that this issue appears to be specific to this one specific person, not a general issue with all Apple Watches as some in this thread are speculating. I certainly have not noticed this behavior on my Watch even with the latest updates.