If you have launched an earlier version of Airport Utility it will notify of upgrade availability. If you want to delete and start over, you can download 6.3.1 from Download AirPort Utility 6.3.1 for Mac that currently downloads a pre-Catalina version which should be upgradable from there.I was on Sierra at that time (finally moved to Mojave just this past week!). Don’t remember if the update was through a notification via App Store / Software Update or, generated by the router, as done for firmware updates, nor do I recall the reason given for it. The October 2018 ”modified” date could have been a background stealth update. Might find some trail breadcrumbs if I pulled up and started poking through Time Machine.
My current Airport Utility Version 6.3.9 (639.9) on Mojave is of equally determinate provenance.
I have not previously looked at the Airport Utility version on any Catalina system. My Catalina Beta system, created by erase and install of Catalina 10.15 Beta in June, has no Mojave history and is now running 10.15.1 (Build 19B68f). Airport Utility reports 6.3.9 (639.13).
The two Airport Utility 6.3.9 builds, 639.9 and 639.13 are not interchangeable. This is probably due to the differing path structures that came with Catalina's dual volume configuration. The Catalina version also adds an Airport Analytics... item in the Base Station menu.