Update deploy automation action to use v1 of external action

[ryanluker]

Description

The publish workflow is using deprecated / soon to be removed functionality. https://github.com/HaaLeo/publish-vscode-extension

It looks like we should be able to go from v0 to v1.

Work

• [ ] Verify the external action v1 will work with repo
• [ ] Update workflow publish file to use new v1
• [ ] Verify next release succeeds