Google says that the process should be automatic.

The process of issuing refunds to Stadia customers for purchases made on hardware, games, peripherals, and subscriptions has begun at Google. This comes a little over a month since Google announced that they were shutting down their online game streaming service. Google still plans on shutting the service down completely on January 18, 2023.

When they made the announcement of Stadia's closure, Google also revealed that they were going to issue refunds to Stadia owners and purchases made via the Google Store along with all games and DLC purchased through the Stadia Store. The time for those refunds to begin is now.

A new Stadia Help article says that refunds began being automatically issued starting November 9. It seems like the only thing that won't be refunded to players will be subscription fees for the Stadia Pro service that were used prior to September 29.

One thing that Google notes here is that users should not contact customer support during this process. Refunds will be rolled out over time. Contacting customer service will not expediate your refunds.

The majority of refunds will be processed by January 18, 2023.