Unfortunately, Google and Apple do not provide any way to connect the two platforms, and they do require that all in-app purchases go through their respective platforms. So the answer is no: if you want to use the app on both platforms, you have to make a purchase on each. Even if you don’t want to continue using it on one platform and want to switch to the other, there’s no technical way to transfer your purchase over.
Also note that hardware adapter requirements are different between the different platforms.
Is Mechanic Access transferable accross different platforms?