In my understanding PubSub filters are supposed to reduce number of messages sent to a specific subscription. We currently observe behaviour that we didn't expect.
Assuming there is a PubSub Topic "XYZ" and a subscription to that topic "XYZ-Sub" with a filter attributes.someHeader = "x" There are 2 messages published to that topic:
First one attributes.someHeader = "a". Second one with attributes.someHeader = "x"
I expect the only message 2 will be delivered to the subscription as message 1 does not match the filter. If it is not the case and still both messages get delivered (what we currently observe):
Filtering in Cloud Pub/Sub only delivers messages that match the filter to subscribers. The filters are applied in the Pub/Sub service itself, not in the client. They allow you to limit the set of messages delivered to subscribers when the subscriber only wants to process a subset of the messages.
In your example, only the message with attributes.someHeader = "x" should be delivered. However, note that as the documentation, the backlog metrics might include messages that don't match the filter. Such messages will not be delivered to subscribers, but may still show up in the backlog metrics for a time.
You do get charged the Pub/Sub message delivery price for messages that were not delivered. However, you do not pay any network fees for them, nor do you end up paying for any compute to process messages you do not receive.