I don’t use Final Cut so not sure if it supports split screen, but even apps that require full screen can be multitasked with Stage Manager now. So you can go do something else. I don’t love Stage Manager, but I use it from time to time for this exact purpose — do something else while a full screen app is also running.
Final Cut does not support split screen multitasking or resizing. and you can't switch away from it while it's exporting to answer a slack message or browse the web, it will just cancel the export.
Interesting, the full screen apps I use just keep going when switching window in Stage Manager, whereas some tasks are normally suspended when switching without Stage Manager. What about slide over? Link doesn't mention it, and Slack can be easily used in a slide over window.