searching for photos on iPhone ignores pictures imported from Photos Mac app

If you want to sync your photos to the iPhone in a way that all titles, captions, keywords, faces, places, albums will be synced to the iPhone and in a full quality, consider to use iCloud Photos to sync the photos.

Then the Photos Libraries on all synced devices will be identical. It would make working with photos across all your devices much easier.

The photos you re syncing from the Finder to your iPhone are just shown in the Photos.app but not properly imported and are limited.

Pictures that are transferred by cable from a computer are not really owned by Photos--they can be shown using Photos, but they don't have the same "rights" with Photos as normal pictures do. "Syncing" by cable is sort of a holdover from earlier days, and it isn't really synchronizing.

On the other hand, pictures that are synchronized using iCloud are exactly the same on all the connected devices-- they carry the same keywords, dates, captions, and so on, even if some devices don't make use of all the features. This is true synchronization-- when you add a picture on your phone, it is automatically added to your Mac and iPad. When you edit a picture on your Mac, the pictures on your phone and iPad show the same edits. This is true synchronization.

To do what you want, keeping captions and keywords the same, you would need to use iCloud to synchronize your phone and Mac. Many of us keep one Library for syncing our favorites with our other devices, and we have other Libraries for archives, and we transfer pictures back and forth between Libraries.

Apple has already phased out My Photo Stream in order to concentrate on more modern methods of transferring pictures. My guess (it's only a guess-- we know nothing about Apple's plans) is that Apple will not add any features to cable transfers in the future.

"And I do not see why ..."

We are just users here. We don't know why Apple has designed things the way they have (and we aren't really allowed to speculate). We just have built up some knowledge about what seems to work and what doesn't.