Apple - App download progress in redesigned Mac App Store (macOS Mojave)

Has this been removed in the redesign?

Yes.

The dedicated Purchases tab present in the older design of the Mac App Store has been moved under the Accounts tab (accessible by clicking on the user's display picture towards bottom left). The new Mac App Store no longer shows the currently downloaded and total size numbers for app installation in progress.

For newly purchased app(s), you can check the download progress by clicking on the profile picture and looking for the app icon(s) towards the top. The apps are listed in order of purchase with most recent purchase shown on top (just like older design of the Mac App Store).

Download progress is also shown on the specific app page in Mac App Store.

However, Mac App Store has adopted iOS style of circular progress bar to show the installation progress which doesn't show the app data downloaded and the total size.

As an alternative measure, you can launch Launchpad.app (by clicking on its icon in Dock, searching in Spotlight or from Applications folder) and still see the progress in terms of data downloaded and total size just below the app icon.

The details of downloads is available in the console app as well as if you use a shell to tail he contents of the install log file. The level of detail is excellent, progress and time estimates are given quite regularly.

 tail -f /var/log/install.log

The other answers to use the graphical interface all match the text based data from this source and logging process.

In the Console app, search for 'storedownload' to filter by progress messages. This is where progress status is logged fairly verbosely by default. The last 10% appears to be reserved for the local installation process.

I was similarly unable to find active download progress. The unlabeled circular progress bar was not cutting it.

I finally found that the download progress is shown if you hover on the Launchpad dock icon: