Looking at your requirements, there are some apps that are worth looking at:
Photoprism, demo is here.
Piwigo, demo is here.
I suggest trying out their demos, so that you can decide what works best for you.
There is also a comprehensive list here with other suggestions.
Edit: A more recent list of photo and video galleries.
I recommend using an online bookmarks manager that enables sharing, display, classification of bookmarks for this purpose.
Some examples include:
Wallabag - it has a paid hosted solution, and also opensource from github if you want to self-host
TagPacker - "free tool to collect, organize, and share your favorite links".
If you decide to self-...