fix: Replace deprecated set-output command

[sjinks]

Description of the Change

GitHub has deprecated the set-output and save-state commands. This PR updates deploy.sh to use the suggested replacement.

How to test the Change

Do a test deployment with generate-zip set to true. Observe that the zip-path output is present.

Changelog Entry

Fixed: Replaced the deprecated set-output command with redirection to $GITHUB_OUTPUT

Credits

Props @sjinks

Checklist:

• I agree to follow this project's Code of Conduct.
• I have updated the documentation accordingly.
• I have added tests to cover my change.
• All new and existing tests pass.

[jeffpaul]

Probably worth checking if this same update needs to be made in the readme/asset update action as well.

[sjinks]

• README.md looks good - there is no ::set-output there;
• release-pull-request.yml - updated.

[cadic]

@sjinks thanks for the update, LGTM.
I've approved the test workflow to run on this PR.