Feat: integrate processor on extensions

[lacroixthomas]

What type of PR is this?

Uncomment only one /kind <> line, press enter to put that in a new line, and remove leading whitespace from that line:

/kind feature

What this PR does / Why we need it:

Integrate the processor client on the extensions behind feature gate

Which issue(s) this PR fixes:

Part of #4190

Special notes for your reviewer:

This is in Work in progress, no need to review yet

[agones-bot]

Build Succeeded 🥳

Build Id: a5107c74-0fb2-41e4-b5ea-47a3b31d8a94

The following development artifacts have been built, and will exist for the next 30 days:

• image: us-docker.pkg.dev/agones-images/ci/agones-controller:1.53.0-dev-eaed611
• image: us-docker.pkg.dev/agones-images/ci/agones-extensions:1.53.0-dev-eaed611
• image: us-docker.pkg.dev/agones-images/ci/agones-sdk:1.53.0-dev-eaed611-linux
• image: us-docker.pkg.dev/agones-images/ci/agones-ping:1.53.0-dev-eaed611
• image: us-docker.pkg.dev/agones-images/ci/agones-allocator:1.53.0-dev-eaed611
• image: us-docker.pkg.dev/agones-images/ci/agones-processor:1.53.0-dev-eaed611
• Linux C++ SDK (build): agonessdk-1.53.0-dev-eaed611-linux-arch_64.tar.gz
• SDK Server: agonessdk-server-1.53.0-dev-eaed611.zip

A preview of the website (the last 30 builds are retained):

• https://eaed611-dot-preview-dot-agones-images.appspot.com/

To install this version:

git fetch https://github.com/googleforgames/agones.git pull/4301/head:pr_4301 && git checkout pr_4301
helm install agones ./install/helm/agones --namespace agones-system --set agones.image.registry=us-docker.pkg.dev/agones-images/ci --set agones.image.tag=1.53.0-dev-eaed611