Source Tree inherited tab support and full screen support via updates to macOS. However, these features are somewhat limited. To enhance support it, would be really helpful to have the option to specify that when opening a new git repo it opens in a new tab rather than a separate window. Also when in full screen if I do a cmd+0 to bring up the repo browser, it would be nice if it supported a split screen popup, rather than opening a separate full screen window. To see an example of what I mean, open the native MacOS mail client in full screen mode. Then click compose new message button in the top right. It will enter split screen mode.

it is worth noting that if you manually setup split screen mode with the repo browser on the right and the main window on the left, when opening a new window from the repo browser, mac OS already directly opens it as a new tab.