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I wonder why the Mac OS desktop app requires 10.15? I'm assuming it's just an electron app.

Not sure about version requirement but you can find that Mac app is written in Swift: https://github.com/mattermost/focalboard/tree/main/mac and Windows application in C# uses WPF: https://github.com/mattermost/focalboard/tree/main/win-wpf

Linux app seems to be just a local server supposedly with web browser as an interface.

Yes, github repo also mentions Catalina (10.15) and XCode 12+.

So, Swift would explain that..

Both these apps contain a few source files and all they do seem to be rendering and handling a webview. The "real" app seems to be this: https://github.com/mattermost/focalboard/tree/main/webapp.