Thank you. That really helps us get an idea of what you are trying to achieve.
As Doug Browning mentioned, you could potentially achieve this outside of Survey123.
If this solution needs to be within S123 (i.e., visible while the form is being filled in), then perhaps JS would work. You could query the second database using the CaseID / AssignedCaseID field(s), then use JS to count the number of items returned since it is an array. Something like this.
The first thing I thought of was "it would be nice to see details on the radios inside the form", but that would require linking of databases, and would further require use of the Inbox feature as that is the only way to populate a repeat (which this data would be). And that seems like it is deviating too much from your current set-up. I thought I would at least mention the idea though since I felt it was a natural suggestion.