tests: add lowest dependency tests (#1067)

Co-authored-by: ihrpr <inna@anthropic.com>

.github/workflows/shared.yml

@@ -29,6 +29,7 @@ jobs:
   test:
     runs-on: ${{ matrix.os }}
     timeout-minutes: 10
+    continue-on-error: true
     strategy:
       matrix:
         python-version: ["3.10", "3.11", "3.12", "3.13"]
@@ -48,8 +49,14 @@ jobs:
 
       - name: Run pytest
         run: uv run --frozen --no-sync pytest
-    continue-on-error: true
 
+      # This must run last as it modifies the environment!
+      - name: Run pytest with lowest versions
+        run: |
+          uv sync --all-extras --upgrade
+          uv run --no-sync pytest
+        env:
+          UV_RESOLUTION: lowest-direct
   readme-snippets:
     runs-on: ubuntu-latest
     steps: