How can I list the last added pictures to the databases? (which is not the same as the last date pictures).
Picasa have an automatic album "Recently added images" which simply shows the last 100 images added to the database (regardless of images timestamp).

How can I achieve the same in digiKam?

It is essential to manage pictures to know what pictures we need to tag and save. For instance, OneDrive saves all pictures taken with the cellphone in a single folder "Camera Roll" whilst there are pictures in my "Downloads" folder and so on. In Picasa I just opened it, list all recent added pictures (in whatever folder in my computer) and the delete and save the ones I want. With digiKam I have to go to each folder and look what pictures are the last one added.

As a new user of digikam I was intrigued by your concern which seemed to be a significant oversight. Then I thought wouldn't it be simple to have a working album for new photos that haven't been processed, rated and sorted. Once you have completed your work on them they could be moved to their appropriate albums. Hoping that would solve your problem.

Why don't you just filter for untagged pictures?