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I need a formal definition for the path measure for stochastic differential equations.

Which textbook or paper should I consult?

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since I don't see any other answers, I will turn my comment into answer.

One Wiener measure and path integrals reference is "Quantum Physics: a Functional Integral Point of View" from here

https://math.stackexchange.com/questions/3255578/schwartz-space-gaussian-measures-and-integration-over-paths?rq=1

For more references in the context of regularity structures and functional integration, see here:

Some interesting series of works on the connection between the two are:

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