I don't have 15. Have you tried it and put it in an Album, because that's where I need it, but it (the caption) only shows up in the library.
In iOS 15 and MacOS 12 once you caption an image you can…- Perform a search using the caption as the search argument
- See the caption anywhere the image appears by doing a Get Info on the image
In MacOS 12 You can make the Captions visible by going to View > Metadata and turning Titles ON (or by pressing ⇧⌘T).
I can find no comparable switch in iOS/iPadOS 15.
(I suspect the option was omitted in iOS because of the iPhone's smaller form factor.)