fix: fix CI tests to correctly use registry from `main` (#3840)

### Description

As part of #3788, we moved to using the registry's `main` branch in CI.
I accidentally didn't include this for other non-required tests that I
didn't realize were failing, and then automerge merged that PR. This
ensures the registry is usable by these other tests

### Drive-by changes

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Are there any minor or drive-by changes also included?
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### Related issues

<!--
- Fixes #[issue number here]
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### Backward compatibility

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implications, e.g. changes that would prohibit deploying older commits
using this infra tooling?

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### Testing

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What kind of testing have these changes undergone?

None/Manual/Unit Tests
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.github/workflows/test.yml

@@ -326,7 +326,7 @@ jobs:
   cli-e2e:
     runs-on: larger-runner
     if: github.event_name == 'push' || (github.event_name == 'pull_request' && github.base_ref == 'main')
-    needs: [yarn-build]
+    needs: [yarn-build, checkout-registry]
     strategy:
       matrix:
         include:
@@ -382,6 +382,17 @@ jobs:
             !./rust
           key: ${{ github.event.pull_request.head.sha || github.sha }}
 
+      # A workaround for relative paths not being supported by actions/cache.
+      # See https://github.com/actions/upload-artifact/issues/176#issuecomment-1367855630.
+      - run: echo "REGISTRY_URI_ABSOLUTE=$(realpath $REGISTRY_URI)" >> $GITHUB_ENV
+
+      - name: registry-cache
+        uses: actions/cache@v3
+        with:
+          path: |
+            ${{ env.REGISTRY_URI_ABSOLUTE }}
+          key: hyperlane-registry-${{ github.event.pull_request.head.sha || github.sha }}
+
       - name: cargo-cache
         uses: actions/cache@v3
         with:
@@ -394,7 +405,7 @@ jobs:
 
   env-test:
     runs-on: ubuntu-latest
-    needs: [yarn-build]
+    needs: [yarn-build, checkout-registry]
     strategy:
       fail-fast: false
       matrix:
@@ -422,6 +433,17 @@ jobs:
             !./rust
           key: ${{ github.event.pull_request.head.sha || github.sha }}
 
+      # A workaround for relative paths not being supported by actions/cache.
+      # See https://github.com/actions/upload-artifact/issues/176#issuecomment-1367855630.
+      - run: echo "REGISTRY_URI_ABSOLUTE=$(realpath $REGISTRY_URI)" >> $GITHUB_ENV
+
+      - name: registry-cache
+        uses: actions/cache@v3
+        with:
+          path: |
+            ${{ env.REGISTRY_URI_ABSOLUTE }}
+          key: hyperlane-registry-${{ github.event.pull_request.head.sha || github.sha }}
+
       - name: Fork test ${{ matrix.environment }} ${{ matrix.module }} ${{ matrix.chain }} deployment
         run: cd typescript/infra && ./fork.sh ${{ matrix.environment }} ${{ matrix.module }} ${{ matrix.chain }}