Fix many instances of contexts and loggers not being propagated (#5340)

This also replaces instances where we manually write "return ctx.Err()"
with "return context.Cause(ctx)" which is functionally identical, but
will also correctly propagate cause errors if present.

pkg/storage/postgres/backend_test.go

@@ -34,7 +34,7 @@ func TestBackend(t *testing.T) {
 	defer clearTimeout()
 
 	require.NoError(t, testutil.WithTestPostgres(func(dsn string) error {
-		backend := New(dsn)
+		backend := New(ctx, dsn)
 		defer backend.Close()
 
 		t.Run("put", func(t *testing.T) {