OBS Studio's settings can be found in the following OS specific locations
Windows: WinKey+R > %APPDATA%\obs-studio
macOS: Cmd+Shift+G > ~/Library/Application Support/obs-studio
Linux: ~/.config/obs-studio
Just Zip the whole folder and you're good. Make sure that all used images and files are at the same location on the new computer, they are not included with the configuration