Show the lastest version of Applications, along with the version you have...
When hovering over a particular application, you can see the version (such as 13.1.5) but there is no info as to whether this is the latest version, was released last week, or was released last year.
You should also allow people to post any bugs or issues related to the latest versions, so others could be saved some heartburn if there is a significant issue. I have been burned several times by buggy releases.

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Franck Payen commented
When you have multiple versions of an app, then the full version of CCDesktop App uses too much space.
I need to keep track of older versions, for plugins or training reasons, and before, I could sort or fold everything behind "latest Ai" + "Latest Ps", now it's just a world of versions here. -
Steve, whenever customer has older version of app, they will see primary CTA of app card in Creative Cloud Desktop as "Update". Also all the new version updates for that app can be found in Updates page of Creative Cloud Desktop.
You can report any bug for any Adobe app following this link:
https://helpx.adobe.com/support.html