It looks like Apple does not expect us to try to manage large photo libraries with the Photos.app. Photos has been designed to work seamlessly across all devices, with the same look and feel on the iPhone as on the iPad or Mac. The storage on the smallest device, probably our iPhone or iPod touch, is the bottleneck for the expected size of the library. i have asked in several Apple Stores at the genie for Apple's recommendation for the size of library, and got the same reply everywhere - keep the size of the library below 20 000 photos at most. Not just because of the storage required, but the processing time, when the library is scanned for object categories, faces, scene categories.
Another reason for the the missing list of albums seems to be the size of the display. Because the smaller devices are having only tiny displays, there is not much screen estate to provide long lists of albums or even menu items. Apple seems currently to reduce the need for detailed graphical user interfaces by making Photos smarter with artificial intelligence tools - we can ask Siri to find and open our albums for us or use the search field. The search is much smarter in Ventura than before (but sadly does not open the album we are looking for, when using the search in Safari).
When you send feedback to Apple, you may want to point out the size of your library, the number of albums and folders, and the need to access the user generated albums from other apps, i.e a web browser, when uploading photos. Siri may be smart and know a lot about sharing photos with friend and family, but really does not understand any of the projects I am working on and the purpose of most of the albums and folders I created.