Hello,
I often find myself getting data in a geodatabase format, and usually first thing I want to do is just get a basic sense of contents. Im sure others do/feel the same way. If you are not familiar with it, the XRay addon for ArcCatalog has been/is great for listing feature classes, fields, domains, etc. The one thing it doesnt provide is feature counts.
I havent been able to find something lightweight and simple to get the feature count information as well, so just spent a few minutes and wrote a very low-tech python code snippet. It will go through a geodatabase and print each feature class name, type, and number of records. It will also total number of feature classes and total feature at end.
Attached is a python code snippet (I saved just as .txt file) that you can load (or copy/paste) to run within Arc Pro or ArcMap in command line. Just make sure to change reference to GDB on line 5. Below is exerpt of results that I ran in Pro