Currently, I have followed the google docs quick start docs for deploying a simple cloud run web server that is connected to AlloyDB. However, in the docs, it all seem to point towards of having to utilize VM for a postgreSQL client, which then is connected to my AlloyDB cluster instance. I believe a connection can only be made within the same VPC and/or a proxy service via the VM(? Please correct me if I'm wrong)
I was wondering, if I only want to give access to services within the same VPC, is having a VM a must? or is there another way?
You're correct. AlloyDB currently only allows connecting via Private IP, so the only way to talk directly to the instances is within the same VPC. The reason all the tutorials (e.g. https://cloud.google.com/alloydb/docs/quickstart/integrate-cloud-run, which is likely the quickstart you mention) talk about a VM is that in order to create your databases themselves within the AlloyDB cluster, set user grants, etc, you need to be able to talk to it from inside the VPC. Another option for example, would be to set up Cloud VPN to some local network to connect your LAN to the VPC directly. But that's slow, costly, and kind of a pain.
Cloud Run itself does not require the VM piece, the quickstart I linked to above walks through setting up the Serverless VPC Connector which is the required piece to connect Cloud Run to AlloyDB. The VM in those instructions is only for configuring the PG database itself. So once you've done all the configuration you need, you can shut down the VM so it's not costing you anything. If you needed to step back in to make configuration changes, you can spin the VM back up, but it's not something that needs to be running for the Cloud Run -> AlloyDB connection.
Providing public ip functionality for AlloyDB is on the roadmap, but I don't have any kind of timeframe for when it will be implemented.