In versions up to 126.96.36.199 it was possible filter all sites with a specific theme, and then (via the button Install to Selected) install a new version of that theme to all of those sites.
In version 4.3xxx this option appears to have disappeared ? Or is that functionality now hidden somewhere else please ?
Currently, the “Install to Selected” button is missing for Manage Themes.
So, even if you search for Inactive themes and select the desired Child Sites, the button will not be displayed as opposed to the Manage Plugins page.
We are planning on addressing this as well. The preliminary plans are to add a separate way to select those sites while also preserving the Lock icon and the protection for the Active themes. We don’t have an exact ETA for this specific change.