synchronization between the physical store and the online website

Hello everyone,

i have a physical shoe store and an online store.

I want full synchronization between the physical store and the online website.

for example, someone buys a product from the online store that will be removed from the inventory of the cash register in the physical store and vice versa, with Full synchronization between inventory and goods between the store cash register and the website, I talked about some companies that sell register machine and he gives me full API access, my question is if there an existing plugin that knows how to receive the API and do Full synchronization between the physical products store and the online store without having to program from scratch.

Thank you for the Help.