Properly unset proxy env if empty

[marcogario]

#2733 did not work correctly for Java because the CLI was expecting the environment variables to be unset and not just empty.

While we make the CLI more permissive, this PR re-introduces the changes in #2733 and patches the analyze action to unset those variables.

Merge / deployment checklist

• Confirm this change is backwards compatible with existing workflows.
• Confirm the readme has been updated if necessary.
• Confirm the changelog has been updated if necessary.

Copilot reviewed 6 out of 6 changed files in this pull request and generated no comments.

Comments suppressed due to low confidence (1)

src/start-proxy-action.ts:103

• This new code path for empty credentials should have corresponding test coverage to ensure it returns early as expected.

  if (credentials.length === 0) {

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