Fix nats_test.go flaky tests (#37976)

Context:
https://fleetdm.slack.com/archives/C019WG4GH0A/p1767759920870649

Looks like some of the tests in `nats_test.go` are failing due to
timeouts. The timeout used for the context in these tests is 5 seconds.
Instead of increasing it, I decided to reduce the number of logs that
are written in tests as well as some sleep statements that I don't think
are needed.
Note that in `nats.go` we use `context.WithTimeout` so that's why the
context deadline exceeded error is raised.

<img width="747" height="373" alt="Screenshot 2026-01-07 at 9 38 04 AM"
src="https://github.com/user-attachments/assets/1a817e8b-6a4a-4d43-9891-07f2791b82ea"
/>

## Testing

Did 5 test runs and measured the test completion time

### Before

<img width="1211" height="230" alt="Screenshot 2026-01-07 at 9 39 59 AM"
src="https://github.com/user-attachments/assets/cf22397b-1962-439c-831f-ef9cde6bf590"
/>

Completion time (avg): 1.23s

### After

<img width="922" height="227" alt="Screenshot 2026-01-07 at 9 38 53 AM"
src="https://github.com/user-attachments/assets/12e1bddd-a257-4313-ab89-e1339374796c"
/>

Completion time (avg): 0.31s

server/logging/nats_test.go

@@ -20,7 +20,7 @@ import (
 )
 
 const (
-	natsTestLogCount      = 1000
+	natsTestLogCount      = 2
 	natsTestDirectSubject = "test.logs.direct"
 	natsTestStreamSubject = "test.logs.stream"
 	natsTestStreamName    = "test-logs-stream"
@@ -68,15 +68,15 @@ func makeNatsServer(t *testing.T) *server.Server {
 	return ns
 }
 
-// makeNatsLogs creates a number of test logs.
+// makeNatsLogs creates test logs.
 func makeNatsLogs(t *testing.T) []json.RawMessage {
 	t.Helper()
 
 	var logs []json.RawMessage
 
-	for n := range natsTestLogCount {
+	for i := range natsTestLogCount {
 		logs = append(logs,
-			json.RawMessage(fmt.Sprintf(`{"foo":"bar %d"}`, n)),
+			json.RawMessage(fmt.Sprintf(`{"foo":"bar %d"}`, i)),
 		)
 	}
 
@@ -235,9 +235,6 @@ func TestNatsLogWriter(t *testing.T) {
 
 		require.Error(t, err)
 
-		// Wait a moment to ensure no messages were published.
-		time.Sleep(100 * time.Millisecond)
-
 		// Ensure no messages were received.
 		lock.Lock()
 		require.Equal(t, 0, seen)
@@ -345,9 +342,6 @@ func TestNatsLogWriter(t *testing.T) {
 
 		require.Error(t, err)
 
-		// Wait a moment to ensure no messages were published.
-		time.Sleep(100 * time.Millisecond)
-
 		// Verify that the stream has no messages.
 		info, err := st.Info(ctx)