Couldn't you configure the existing panel to do what you want? Add and remove widgets and resize it and you should have what you need.

As far as I'm aware, no launcher (in the style of KRunner) exists which has all those features.

With some effort, you could implement a lot of this functionality using a "generic" launcher (like rofi, for example), but integrating a system tray will be close to impossible (unless you're willing to write a program which acts as a system tray and provides those launchers with enough information to display a useful representation of the tray, could be cool).

You can create a panel in edit mode and put whatever you need (clock, system tray, application menu) on it. Set size to fit content and make windows go below which results in a tiny floating panel for example.

IIRC krunner works as a commandline tool, so maybe you could do what you want with something like yakuake, or even make a wrapper for krunner with those additional options.

It seems like something I could use as well. I'll note it down to take a look later.