"Purchased" is not longer a playlist within the Library of the side bar in Apple Music

You could create a "Smart Playlist". This is a saved search that will automatically show, or stop showing, songs that [do not] match the criteria. It works on a similar principle to a "Smart Folder" in the Finder.

• Select File > New > Smart Playlist.
• For one of your rules, select Purchased from the pop-up menu on the left, and is true from the pop-up menu in the middle. ("Purchased" in this context means "purchased from the iTunes Store"; this rule will not match any music that you purchased in other ways: from Amazon's MP3 Store, on CD, etc.)
• If you need more rules, hit the "+" and add them.
• When you're done, if you have multiple rules, go up to the line that says "Match ____ of the following rules" and make sure that all (not any) is selected.
• Select OK to close the dialog, then rename your new playlist anything you like.

To my knowledge, no, not as it was. However, you could create a smart playlist with a "Date Added" "Is In the Last" [however many days back you want it to show]. That would give you something of the same function.

Regards.

cuznmatt wrote:

Is there a way to bring this back. It was an effective way to quickly find the songs I most recently purchased in a "list" rather than the thumbnails in recently added.

Under the Account menu item, you can list albums and songs by "Purchased."

Alternatively, when you list all Songs in your Music Library, one of the columns you can specify under View => Show View Options is "Purchase Date." You can then sort by that column and select all purchased songs and put them in a Playlist.