Is your feature request related to a problem? Please describe.
Currently, the SIDECAR_IMAGE environment variable can be set in the Agones controller, but it cannot be easily modified when installing Agones via Helm. This limitation forces the image registry to follow the common Agones settings, and it cannot be customized through deployment commands, arguments, or flags. For instance, if there is a need to use a different registry for the sidecar image, such as in cases where the sidecar image must be pulled from a private registry due to issues like those described in issue #3978, the current setup does not provide an easy way to achieve this.

Describe the solution you'd like
I would like to see the introduction of a Helm chart variable that allows the SIDECAR_IMAGE to be configured independently. This would enable users to specify a different image registry for the sidecar without affecting the main Agones configuration. It would provide more flexibility in managing image sources, especially in scenarios where different registries are required for different components.

Describe alternatives you've considered
The current alternative is to manually modify the deployment after the Helm installation or to maintain a custom fork of the Helm chart that includes the desired changes. However, these approaches are less efficient and more error-prone compared to having an official Helm variable for this purpose.

Additional context
This feature would be particularly useful in situations where the sidecar image needs to be pulled from a private registry, as in the case described in issue #3978. It would allow for easier maintenance and customization of Agones installations in environments with specific registry requirements.