fix(tests): ensure test isolation in server mode (#3737)

Propagate test IDs from client to server via HTTP headers to maintain
proper test isolation when running with server-based stack configs.
Without
this, recorded/replayed inference requests in server mode would leak
across
tests.

Changes:
- Patch client _prepare_request to inject test ID into provider data
header
- Sync test context from provider data on server side before storage
operations
- Set LLAMA_STACK_TEST_STACK_CONFIG_TYPE env var based on stack config
- Configure console width for cleaner log output in CI
- Add SQLITE_STORE_DIR temp directory for test data isolation

.github/workflows/integration-auth-tests.yml

@@ -85,7 +85,7 @@ jobs:
           cat $run_dir/run.yaml
 
           # avoid line breaks in the server log, especially because we grep it below.
-          export COLUMNS=1984
+          export LLAMA_STACK_LOG_WIDTH=200
           nohup uv run llama stack run $run_dir/run.yaml > server.log 2>&1 &
 
       - name: Wait for Llama Stack server to be ready