Global vs site configuration for theme?

I’ve installed the core themes from I was hoping to add our university logo and footer HTML to each of the themes globally so they are set for sites that choose one of these themes but it appears that the logo and footer HTML is edited for each site. Is that correct? If we want to have a consistent university logo and footer we will need to manually add that to each site?

Once you have uploaded an asset to use as a logo for one site, it should be available for all the sites on your installation.