I found this discourse useful, as it contained several examples
I discovered I had added a variable “$” that was unnecessary. When I used a constant, it passed the value. The expression (e.g., rand()) still is not passing the value. The constant also will not update now (cleared cache, incognito run). There were notes that, previously, expressions could not be passed as values in the URL, but it also sounds like they now can?
I would like to avoid using the external app solution, because those dependencies are too risky if they should have unexpected down time, etc.