Automate npm dist-tags (#48982)

* Remove outdated comment

* Add logic for automating npm dist tags

* Fix deprecated GitHub action output command

* Update .github/workflows/release-embedding-sdk.yml

Co-authored-by: Denis Berezin <denis.berezin@metabase.com>

* Add comment and correct 51 dist tag

---------

Co-authored-by: Denis Berezin <denis.berezin@metabase.com>

.github/workflows/release-embedding-sdk.yml

@@ -3,7 +3,6 @@ name: Release Metabase Embedding SDK for React
 on:
   workflow_dispatch:
     inputs:
-      # TODO: Add a version validation, so the workflow won't fail when publishing to npm
       branch:
         description: "Branch we want to release the SDK from"
         type: choice
@@ -51,7 +50,7 @@ jobs:
         id: current-sdk-version
         run: |
           VERSION=$(jq -r .version ./enterprise/frontend/src/embedding-sdk/package.template.json)
-          echo "::set-output name=sdk_current_version::$VERSION"
+          echo "sdk_current_version=$VERSION" >> $GITHUB_OUTPUT
 
       - name: Get next SDK patch version
         id: new-sdk-version
@@ -249,7 +248,13 @@ jobs:
         run: |
           cd sdk
           echo //registry.npmjs.org/:_authToken=${{ secrets.NPM_RELEASE_TOKEN }} > .npmrc
-          npm publish
+          # Please keep the value in sync with `inputs.branch`'s release branch
+          npm publish --tag ${{fromJson('{"master": "canary", "release-x.51.x": "51-stable"}')[inputs.branch]}}
+
+      - name: Add `latest` tag to the latest release branch (`release-x.51.x`) deployment
+        if: ${{ inputs.branch == 'release-x.51.x' }}
+        run: |
+          npm dist-tag add @metabase/embedding-sdk-react@${{ env.sdk_version }} latest
 
   git-tag:
     needs: [publish-npm, determine-version]