If you wish to have different URL's for each client of yours, you may consider incorporating a
dispatch.yaml file with the help of
Wildcard mappings which will route the specific URL patterns according to your own rules. In your specific use case, you may consider to do this at the
application layer, using the same dispatch.yaml file mentioned above.
The aim is to route each request through the dispatch file based on the URL supplied as shown in the last example
here. This in return will allow you to have distinguishable URL's for the different or a specific service that you set.
As for the Cloud SQL instance/database connectivity, as all clients are using the same codebase, you would need to manage the connections programmatically.
Lastly, I would like to mention that this information is intended to provide you some sort of context/direction on how you can go about achieving the set up you have discussed. You may feel free to consult the provided documentation for further in dept considerations of what has been mentioned for your use case.