Cloudflare Pages takes over entire sub-domain - No precedence for paths to Workers

We are stuck with a serious issue where we moved our entire static client app for serving under a sub-domain like this, via Cloudflare Pages:

… and then discovered that Workers listening on a route like this:

… never triggered or fired. We simply got a 404, since it seems that CF Pages assumes everything under is a static asset.

How can I give Workers higher precedence to run first, before Pages?