It's been a few days now, a little less than three weeks if I'm not mistaken, that Ubuntu 23.10, currently in development, has started to offer the App Store new based on Flutter. In September of last year we publish an article about this store, one that was being developed by the community and greatly improved current Ubuntu Software, but what we're seeing in Mantic Minotaur's Daily Builds is a bit puzzling. It is true that it is still in development.
What is happening now is what the header screenshot shows, and what should happen is what is in the next screenshot or the linked article. The actual Ubuntu Software is a modified version of GNOME Software designed to prioritize snap packages, but still shows the option to download the DEB or APT version. However, although the community store (Flutter) also displays DEB packages in a separate tab, what we currently find under the name App Store does not.
The “App Store” will be renamed “Ubuntu Store” or something similar
According to what Tim says, this is all "under construction", and support for DEB packages will be included before the release of Ubuntu 23.10:
This project is still in the construction phase and right now we are focusing on the main features. I'm optimistic that by the 23.10 release our new approach to rankings and deb support will have landed, as well as many more improvements.
He is optimistic, but not 100% sure that support for DEB packages will arrive before the release of Mantic Minotaur, well, is that something to worry about or not? You will have to trust them. Also, as they explain even with a Spider-Man meme, when this store launches there will be 3: the current Ubuntu Software, the future one based on Flutter, and GNOME Software, the official Project GNOME store. It won't be due to options. What is scary is that in Mantic Minotaur's Daily Build only one appears, the one that only shows snaps.
If we assume that the Ubuntu store will be based on Flutter and that it will support DEB packages, the only thing left to know is what name they will launch it under. They would like it to be the App Store, but if they end up using that name they will have problems with Apple. In this thread They even refer to it as "Ubuntu Store", "App Center" and "App Bazar" are proposed, and we will have to wait a few days to a few weeks to find out its final name, and what ends up happening with the DEB software.