When you preview a theme you are seeing a "default sidebar display" that does not contain actual widgets. When you activate a new theme the widgets you previously used will be there.
No content is ever lost when switching themes and it takes only minutes to do this > appearance > Themes > Select theme > click "activate" when the thumbnail image appears. There may be some in the Inactive Widgets box > Appearance > Widgets > Inactive Widgets box that you will need to install in the sidebar or footer areas for widgets. Simply drag and drop them into place, click to open, click "save" and 'close" and that's it.
What's more important is the maximum displayed image width and sidebar width when switching themes. The images will remain in your Media Library.These are the maximum displayed image widths by theme. These are the sidebar widths by theme.