[stable2509] Backport #11461 (#11551)

Backport #11461 into `stable2509` from BDevParity.

See the
[documentation](https://github.com/paritytech/polkadot-sdk/blob/master/docs/BACKPORT.md)
on how to use this bot.

<!--
  # To be used by other automation, do not modify:
  original-pr-number: #${pull_number}
-->

Co-authored-by: BDevParity <bruno.devic@parity.io>

Author: paritytech-release-backport-bot[bot]

.github/workflows/release-80_publish-crates.yml

@@ -291,7 +291,7 @@ jobs:
 
           if [ "$REGISTRY" = "staging.crates.io" ]; then
             cat >> ~/.cargo/config.toml << 'EOF'
-          [registries.crates-io]
+          [registries.staging]
           index = "sparse+https://index.staging.crates.io/"
           EOF
           else
@@ -305,7 +305,8 @@ jobs:
         if: inputs.resume_from != 'push'
         shell: bash
         env:
-          PARITY_PUBLISH_CRATESIO_TOKEN: ${{ inputs.registry == 'staging.crates.io' && secrets.STAGING_CRATES_IO_API_TOKEN || secrets.CRATES_IO_API_TOKEN }}
+          PARITY_PUBLISH_CRATESIO_TOKEN: ${{ secrets.CRATES_IO_API_TOKEN }}
+          PARITY_PUBLISH_STAGING_CRATESIO_TOKEN: ${{ secrets.STAGING_CRATES_IO_API_TOKEN }}
           DRY_RUN: ${{ inputs.dry_run }}
           REGISTRY: ${{ inputs.registry }}
           PUBLISH_JOBS: ${{ inputs.publish_jobs }}
@@ -316,13 +317,18 @@ jobs:
             PARALLEL_ARGS="-j $PUBLISH_JOBS --no-verify"
           fi
 
+          STAGING_ARG=""
+          if [ "$REGISTRY" = "staging.crates.io" ]; then
+            STAGING_ARG="--staging"
+          fi
+
           if [ "$DRY_RUN" = true ]; then
             echo "DRY RUN - Not actually publishing crates"
             echo "Target registry: $REGISTRY"
-            parity-publish apply -p -d $PARALLEL_ARGS
+            parity-publish apply -p -d $STAGING_ARG $PARALLEL_ARGS
           else
             echo "Publishing crates to $REGISTRY..."
-            parity-publish apply -p $PARALLEL_ARGS
+            parity-publish apply -p $STAGING_ARG $PARALLEL_ARGS
             echo "Crates published successfully to $REGISTRY!"
           fi