Fix local setup issues

[ialidzhikov]

How to categorize this PR?

/area dev-productivity
/kind bug

What this PR does / why we need it:
This PR performs the following changes from the registry-cache extension which are applicable also to this extension:

• Fix make extension-up gardener-extension-registry-cache#277
• Fix skaffold tag generation to generate a new tag on code changes (without local commit) gardener-extension-registry-cache#279

Which issue(s) this PR fixes:
N/A

Special notes for your reviewer:
N/A

Release note:

An issue causing `make extension-up` to fail to patch the ControllerDeployment is now mitigated.

An issue causing `make extension-up` to do NOT generate a new tag for local source code changes is now fixed.

[gardener-prow]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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