Does comma placement before/after a prepositional phrase alter a sentence's syntactic grammaticality?

I am looking to understand when a comma, involving a prepositional phrase, shifts from being a mere stylistic choice to a factor that determines the strict grammaticality of a sentence. For standard descriptive endings, a comma feels purely optional or stylistic: "We decided to meet at the park, near the old oak tree." "We decided to meet at the park near the old oak tree." However, when we move…