That’s too bad as that’s my flow: test changes on a local testing site, then push to the live site. I don’t have a 3rd site (ie, a proper “staging” site which is publicly accessible but not the same as the live site).
Maybe this could be supported if the plugin supported one-way communication (ie, the localhost staging site communicating with the public live site).
I bet adding support for localhost sites will be a lot of work, maybe too much work to merit doing. But just letting you know it’s what I was hoping for.

I have a localhost staging site that I activated this on and got the warning “WordPress Data Merge & Sync: sqlite3 extension is not enable. This extension is required.”