I use Bridge as the file manager for all my thousands of photos and finding folders by name is not a problem. But I recently realised that there is an option to add tags to every photo when saving it in Photoshop. So I have trialled this with the contents of a few recent folders, assuming that then there would be some kind of search engine in Bridge which would allow me to find the relevant photos of e.g. my stepson regardless of what folder he might be in by looking for his name. But I can find no such way of searching and thus I am wondering what is the point of the tags option when saving a photo? Am I missing something or is the only way to set up searching at this granular level to use the Keywords Panel in Bridge? It doesn't make sense to me for Photoshop seemingly to offer something that has no user value.
Have you tried the advanced search function in Bridge? Open it in the top left search drop down or Cmd/Ctrl+F
This feature allows you to select which folder to search and which field to search. You can also opt to search all subfolders.
There is no such thing as tags in Bridge. Are you talking about keywords? Be aware that both Mac and Windows have tags available but they are different things and not cross-platform.
Shall we be realistic here?
As Lumigraphics has stated, THERE ARE NO TAGS IN BRIDGE. There are Keywords. Keywords are a universal field in all files to place words that mean something to the user and can be used to search for those words across the many files they have. They are most commonly used in images, but they can also be used in Word files, PDFs, FileMaker Pro files, and any file can have keywords.
TAGS are used on the Mac OS to delineate how a file has been categorized by the user and actually look like this before they have been subjugated by folks who alter an image to display how they wished them to look.
You have a dozen "tags" in your sample. Your creation will work fine with a dozen, maybe two dozen "tags." But many people who have keywords have maybe one hundred, maybe two hundred, and this does not even get to the sub-keywords.
"Tags" can also go by the name "Lable" as here in Bridge and can be used in conjunction with, or separately from, Ratings. Labels are not universally joined identification because any Label you put in Bridge may not always be understood by Lightroom, and if you change the names of the Labels, they are typically shown as "white" by another application as well as the Finder (if they are seen at all).
Keywords, on the other hand, will show up in any application that has the ability to show or find Keywords. The region you show for Tags, is for the Finder, NOT Bridge.
Tags are a macOS feature and not supported in any way by Adobe. You can search in the Finder or in software that supports this feature. Tagged files will not show those tags if they are moved to a Windows system.