Just want to inform you that the cause for my delay-issue is editing a lot of entries and add new rich icons to them. There more entries I edit the slower the Windows desktop app gets. That's why the browser extensions (tested in Firefox and Vivaldi) get slow, too.
The only solution is to close 1Password for Windows. After restarting the app and the browser extensions work as they should until I edit entries again.
Support is informed and Devs are involved. Thanks again @Dayton_ag, @Blake and David for the great communication via email.
@DenalB: Thank you for posting an update here!
We will definitely take a closer look at what is going on and get back to you. Thanks again!
Thank you all for the support!
Thanks so much for all your help @DenalB!