When using KDE Plasma in a Wayland session, Plasma can show a titlebar and borders around the Ulauncher window:

Plasma v6 or newer

Make sure you are using Ulauncher 6 (currently in beta) or newer and have gir1.2-gtklayershell-0.1 installed.
It should work automatically with no additional workarounds.

Plasma v5

If you are using Plasma version 5, you also need to use Ulauncher v6, but Plasma v6 doesn't support Layer Shell. Instead you need to add a workaround for Ulauncher in the system settings:

Go to:
System Settings > Window Management > Window Rule > Add New
Window class (application): "Exact Match" "Ulauncher"
Match whole window class: No
Window types: Normal Window

Then "Add Property..." and select "No titlebar and frame" and "Keep above other windows".

Lastly, click "Apply"

This should work (did for me). If not, make sure you set everything exactly as in the screenshot.

If this looks different for you, maybe you have an even older version of Plasma. Then you can try [this guide](Outdated guide to do this (good enough to find how to do it still): https://medium.com/@CodyReichert/how-to-hide-title-bars-in-kde-plasma-5-348e0df4087f)

Note however that this workaround will also apply to the Ulauncher preferences window, where we want the titlebar (can't close or move it without it). Ulauncher has no plans to support Plasma v5 or older, so this is as good as it's going to get.