[cherry pick to 1.22] Start the informerFactory in the ControllerContext

[sdmodi]

What type of PR is this?

/kind bug

What this PR does / why we need it:

Cherry picking pull request #103951 to release-1.22 branch.

Which issue(s) this PR fixes:

Fixes #

Special notes for your reviewer:

Does this PR introduce a user-facing change?

Additional documentation e.g., KEPs (Kubernetes Enhancement Proposals), usage docs, etc.:

[k8s-ci-robot]

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[k8s-ci-robot]

Hi @sdmodi. Thanks for your PR.

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[puerco]

/ok-to-test

[sdmodi]

/retest-required

[cheftako]

/release-note-none
/lgtm
/approve

[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: cheftako, sdmodi

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[cheftako]

/priority important-soon

[savitharaghunathan]

/test pull-kubernetes-integration

[puerco]

Thank you @sdmodi!
/lgtm

[k8s-triage-robot]

/retest
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