Hi there!
I'm using the Platform for some years, and I see it's changing but the dialog window for getting new apps is still without any search box, however it got 10 categories there and 200+ item which are hard to find quickly when you need it.
Dialog window of PA Updater (aka PA Directory) is shown below
https://vgy.me/kmDfl1.png
Hope it would be invented in the future releases of the Platform!
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It is listed in the PortableApps.com Platform Bug Report and Feature Tracker thread under Upcoming Features as "Search App Directory".
But please be aware there is no indication of when it will be done, this only says that it is planned for some time in the future.