Wonder if you can 'and' in a not 0 file count also?

Yep, this works

"C:\base folder\" !childfilecount:1 !childfilecount:0

but nkormanik found the shorter

"C:\base folder\" childfilecount:>1

Sooo many additional options as well.  Never knew.

Indeed, Everything just keeps on giving. It is in that sweet spot of having a simple looking UI yet is very rich in features and syntax options. I actually didn't know about the childfilecount: command until I read this thread and thought "I bet Everything has some way or other to do this". 

I noticed there is a difference between

"C:\base folder\" !childfilecount:1 !childfilecount:0

and

"C:\base folder\" childfilecount:>1

The former lists both the matching folders and their files, but the latter only lists the folders. This means that there are two different workflows to choose among
1. find the list of matching folders and then manually open matching folders in Explorer one at a time and delete unwanted files.
2. find the list of all *files* in matching folders, sort the Everything list by Path and manually delete unwanted files one at a time directly in Everything.
For workflow 2 the search could be one of these

"C:\base folder\" !childfilecount:1 !childfilecount:0 file:

"C:\base folder\" !childfilecount:1 !childfilecount:0 ext:mp3

"C:\base folder\" !childfilecount:1 !childfilecount:0 audio:

Had a fool around with EBO for something to do.

The OP mentioned TreeSize.  From idle curiosity, I entered it into AlternativeTo and found WizTree, which claims to be the fastest of its type and certainly seems like it, much faster than WinDirStat, but doesn't address the more-than-one-file question.

Also, FolderSizes, which apparently can:

You can now search for folders based upon the number of files and/or subfolders they contain. This criterion can be based upon the immediate file/folder count, or the aggregate file/folder count (which includes counts from nested subfolders).

But it's a heavy-duty tool - 27MB and $60.

Nir Sofer's SearchMyFiles can show number of files per folder in Summary mode, but you'd still have to eyeball the report, or post-process it.

A quick note on what the application is with the present request: Music Collection Maintenance.

$35 https://www.bolidesoft.com/audiocomparer/

Find and Remove Duplicate Songs Automatically

Audio Comparer is a simple tool that will help you to automatically find and remove duplicate songs in your collection. The program works with Windows Vista/7/8/10 and can compare audio files by their actual sound data. Audio Comparer listens to your audio files and remembers all of them. After that, it compares how they sound and places similar-sounding files into groups where you can select which file you want to delete and which to leave on your hard drive. This way our program can even detect duplicates with wrong or missed tags filled. Also, Audio Comparer is able to detect the same song stored in different audio formats (for example, FLAC and MP3).

Also: https://alternativeto.net/software/audio-comparer/