Cloud Run mapping services by URL path (using custom domain and wildcards)

Question

I've been trying to migrate my solution from Google Cloud App Engine to Google Cloud Run and have been struggling a lot.

I have 3 services in app engine for each staging environment, let's call them api, front1, front2. front1 has custom domain name assigned www.example.com, as well as staging subdomain www.dev.example.com. Using dispatch.yaml rules I route requests to appropriate services, for example: requests containing api/* are routed to api service, default path routes to front1, /foo* routes to front2. Everything is working there perfectly well, however, hosting the solution on Cloud Run would decrease the costs a lot.

So at the moment, I am really struggling to understand how could I fully replicate this behavior in Cloud Run. I've tried following firebase routing, but it requires to host an app on Firebase as well and doesn't route all traffic for route /api/** to my api service.

I've tried following this article, but I cannot select my service since I selected Internet Network Ednpoint Group option for backend type, which only can point to a single url. Also, I am not sure if it will support wildcard routing there.

I'd highly appreciate any help here, I am totally out of options at the moment.