fix: harden storage semantics (#4118)

Fixes issues in the storage system by guaranteeing immediate durability
for responses and ensuring background writers stay alive. Three related
fixes:

* Responses to the OpenAI-compatible API now write directly to
Postgres/SQLite inside the request instead of detouring through an async
queue that might never drain; this restores the expected
read-after-write behavior and removes the "response not found" races
reported by users.

* The access-control shim was stamping owner_principal/access_attributes
as SQL NULL, which Postgres interprets as non-public rows; fixing it to
use the empty-string/JSON-null pattern means conversations and responses
stored without an authenticated user stay queryable (matching SQLite).

* The inference-store queue remains for batching, but its worker tasks
now start lazily on the live event loop so server startup doesn't cancel
them—writes keep flowing even when the stack is launched via llama stack
run.

Closes #4115 

### Test Plan

Added a matrix entry to test our "base" suite against Postgres as the
store.

.github/workflows/integration-tests.yml

@@ -66,12 +66,12 @@ jobs:
   run-replay-mode-tests:
     needs: generate-matrix
     runs-on: ubuntu-latest
-    name: ${{ format('Integration Tests ({0}, {1}, {2}, client={3}, {4})', matrix.client-type, matrix.config.setup, matrix.python-version, matrix.client-version, matrix.config.suite) }}
+    name: ${{ format('Integration Tests ({0}, {1}, {2}, client={3}, {4})', matrix.client, matrix.config.setup, matrix.python-version, matrix.client-version, matrix.config.suite) }}
 
     strategy:
       fail-fast: false
       matrix:
-        client-type: [library, docker, server]
+        client: [library, docker, server]
         # Use Python 3.13 only on nightly schedule (daily latest client test), otherwise use 3.12
         python-version: ${{ github.event.schedule == '0 0 * * *' && fromJSON('["3.12", "3.13"]') || fromJSON('["3.12"]') }}
         client-version: ${{ (github.event.schedule == '0 0 * * *' || github.event.inputs.test-all-client-versions == 'true') && fromJSON('["published", "latest"]') || fromJSON('["latest"]') }}
@@ -84,6 +84,7 @@ jobs:
         uses: actions/checkout@08c6903cd8c0fde910a37f88322edcfb5dd907a8 # v5.0.0
 
       - name: Setup test environment
+        if: ${{ matrix.config.allowed_clients == null || contains(matrix.config.allowed_clients, matrix.client) }}
         uses: ./.github/actions/setup-test-environment
         with:
           python-version: ${{ matrix.python-version }}
@@ -93,11 +94,16 @@ jobs:
           inference-mode: 'replay'
 
       - name: Run tests
+        if: ${{ matrix.config.allowed_clients == null || contains(matrix.config.allowed_clients, matrix.client) }}
         uses: ./.github/actions/run-and-record-tests
         env:
           OPENAI_API_KEY: dummy
         with:
-          stack-config: ${{ matrix.client-type == 'library' && 'ci-tests' || matrix.client-type == 'server' && 'server:ci-tests' || 'docker:ci-tests' }}
+          stack-config: >-
+            ${{ matrix.config.stack_config
+                || (matrix.client == 'library' && 'ci-tests')
+                || (matrix.client == 'server' && 'server:ci-tests')
+                || 'docker:ci-tests' }}
           setup: ${{ matrix.config.setup }}
           inference-mode: 'replay'
           suite: ${{ matrix.config.suite }}