The only (and most accurate) place for files to be listen in projects, is… in the project file. So I guess that the only option (well, the easiest without e.g. manually scanning all project files) us, to open the project file and browse for the missing file(s). If more missing files are in the same folder a the first missing, PD will see that and open them. Important is to SAVE the project to prevent this form happening again, at least if you don’t intend to move the files around again. If you decide to ignore the missing files, PD will open the project as, you say, without these files. If you the save the project, you will definitely lose the list of files originally used!
The project packing option is there to make sure that all used files are kept together with the project file. As long as you move the folder in its completeness, all project files will be found at open time.
It is what it is….

Thank you.

In recent projects I do the Packing but none of the older projects.

Is there just one project file that has all the used images, video?

There must be one somewhere so the panel comes up and asks to browse for those that aren't therre.

Where does it get that info?

The saved project file does contain the links of ALL files used in the timeline, but also of ALL files that are in the project media-room. It also contains the links and additional information for titles, subtitles, LUTs, etc. etc. As far as I know and have seen, there is no other place where CL keeps project-related information. The project files also contains a record of all the editing you have done, without touching the original files.
Once you open a project, it will make the files available in the media room and in the timeline, as they were at the moment of the project save, using the links recorded. If a file is not found at the place where the link points to, PD will show a message and allow you to browse (or ignore, or ignore all). You may have seen that, otherwise give it a try.
PD gives this not found, browse or ignore (ignore all) message for each of the files not found. In subsequent not found situations, PD will also look in the folder where previous files have been found, and automatically include and make them available.
Have look at: https://help.cyberlink.com/stat/help/powerdirector/21/win/enu/04_00_00_pdr_projects.html?q=project+file