There has never been a font from Adobe's Type Library with a name beginning with California during the Creative Suite timeframe. Any such font must have been installed by the operating system or some other application.
There is a family of fonts named Californian FB distributed with some versions of Microsoft Office. Maybe those are the fonts that you are looking for. The same family of Californian FB fonts is also available with the cloud-based Adobe Fonts (previously Typekit) service which is available to you as a Creative Cloud subscriber.
If you provide the names of the other “missing” fonts, perhaps we can assist you further. But as Steve Werner indicated, installing a newer version of Adobe software does not uninstall any fonts that had been installed on your system by Adobe or any other software.
In the general case, if migrating to a new computer system, you should always copy any non-system fonts from the old to the new system. Even more important is that you regularly backup your computer such that if there are resources that are either lost or damaged on your current system or not otherwise available on a newer system, you can directly access those files from your backup. You do regularly backup your systems, don't you?
- Dov