Handle SDKContextClass client initialisation internally (#34146)

* Handle SDKContextClass `client` initialisation internally

Rather than via MatrixChat - this is predominantly for Lifecycle tests as they don't use a MatrixChat and it doesn't make much sense for this component to own this state.

* Fix tests

apps/web/test/unit-tests/components/structures/PipContainer-test.tsx

@@ -112,7 +112,7 @@ describe("PipContainer", () => {
         sdkContext = new TestSDKContext();
         // @ts-ignore PipContainer uses SDKContext in the constructor
         SDKContextClass.instance = sdkContext;
-        sdkContext.client = client;
+        sdkContext._client = client;
     });
 
     afterEach(async () => {