I found a solution for us... (just an option for other stakeholders)
Yesterday I've created a TestComplete script method to add a test item name and its result into a csv file.
This method is called by the OnStopTest-Event for each test item and the current result is flagged by the OnLogError-Event.
New test items will be appended to csv file (its result in the correct test run column), disabled test items which are already known in csv file, register a space.
The csv file handling will be executed only when a entire test suite run is in progress (not if only a single test item is executed).
csv file content example:
Testrun ;TR1 ;TR2 ;TR3 ;TR4 ;TR5
TestItem1 ;passed ;passed ;failed ;passed ;passed
TestItem2 ; ;failed ;passed ;passed ;passed
TestItem3 ;passed ; ; ;passed ;failed
TestItem4 ; ; ; ; ;passed
...
At the beginning of a test suite run (or end) TC edits the csv file and adds " ;" to each line = existing but not executed test items are registered - and new results are separated in a new csv column
After a test suite run is finished, I edit the csv file manually with conditional formatting rules, then it looks like the "NetSparker"-screenshot.