Revert #124 and #135 (#139)

This seems to be causing a lot of weirdness, presumably because there's
another missing thing like in #135, but I don't know what it might be and
it feels like it might take a while to find. Backing these changes out
to fix develop while we sort it out.

Fixes https://github.com/element-hq/element-web/issues/28179

test/stores/VoiceRecordingStore-test.ts

@@ -31,7 +31,7 @@ describe("VoiceRecordingStore", () => {
 
     const mkStore = (): VoiceRecordingStore => {
         const store = new VoiceRecordingStore();
-        store.useUnitTestClient(stubClient);
+        store.start();
         return store;
     };