Don't have a solution, but I'm having the exact same issue! I'm using ArcGIS Online.
I've attached a picture here of a map pop-up side-by-side a query widget that is failing to show the contents (Arcade block) of the pop-up.
Like you said, I know the query results DO work with a text block configured to return Arcade expressions (with html formatting set in the text content "builder" where you can choose colors, font size, etc.), so it seems that the Arcade block specifically is the issue.
Edit: Bad news (or good news in terms of me not wasting any more of my time on this?). I just put Esri's Arcade examples map (relevant blog post) into Experience Builder along with a query widget, and it also doesn't return the Arcade block they've put in there. It only returns the two text blocks.
A workaround (like I mention above) would be to use a text content block that you insert Arcade expressions into. When you're in the text block editor window, click "Source" and it will allow you to edit the html. There are more tags you can use than what's provided through the buttons at the top of the window. Note that when you're viewing the Source, the OK button will gray out. Just click the source button again and then you can click OK.
Really hope someone from Esri can explain this or point to a bug page or something.
