Please know Republic does nothing to restrict receiving SMS from international numbers. That said, the process of getting an SMS message from Korea or anywhere else outside the U.S. with the possible exception of Canada varies widely and to be candid is simply not always reliable. There are a lot of potential points of failure between the message originating in Korea and your Republic phone.
There is no particular reason to believe Google Voice will be a solution, however, I sincerely hope I’m wrong about that. Candidly if one needs to be able to regularly and reliably receive SMS from international numbers, one needs a number with one of the large wireless carriers.
Has your boss considered using an alternative messaging app such as WhatsApp or Signal or an app designed for collaborative teams like Slack? Using such apps would mean everyone would need to agree to use the same app. On the other hand, it would be a far more secure means of communication particularly if sensitive proprietary information might be involved.