That was a strange issue, but it's now solved by changing the way the app opens the action center (now it executes ms-actioncenter: instead of triggering the keyboard combination Win + A).
The updated app is available through release 1.0.5.

Thank you for such a prompt response! Unfortunately, the issue still persists with version 1.0.5 on my machine. BTW hitting Win + A or executing ms-actioncenter: in the file explorer does not trigger the issue.

Could you give 1.0.6 a try?

The underlying reason for this bug might be, that the old version of the program together with the wrongly mapped action center key in the German keyboard layout triggers a so called Office key: https://twitter.com/h0x0d/status/1140784669962584066?s=09

Could you give 1.0.6 a try?

I tried version 1.0.6 and the Office App no longer opens. Good! However, the key no longer functions as a toggle. That is it opens Action Center, but using the key again will not close it afterwards. This is different to how Windows+A works.

tl;dr: It is finally fixed in 1.0.7.

The reason for the behavior of 1.0.6 was that I switched to just executing ms-actioncenter: which seemed to be more reliable (but one-way).
However I just took a further look and discovered, that since Windows 10 v1903 Shift+Ctrl+Win+Alt is the "Office key" (which can open different Office apps). This shortcut collided with Shift+Ctrl+Win+Alt+F21, which gets triggered by the surface keyboard when pressing the action center key. For 1.0.7 I rearranged some logic in the app to prevent this.