Please address the comments from this code review:
## Individual Comments

### Comment 1
<location> `ext/sse/server.go:46` </location>
<code_context>
+	return s
+}
+
+func (s *Server) keepAlive() {
+	if s.keepalive <= 0 {
+		return
</code_context>

<issue_to_address>
The keepAlive logic may incorrectly identify active clients as dead.

The conditional appears inverted; clients should be marked dead only if lastSeen is before timeout. Please update the logic accordingly.
</issue_to_address>

Please address the comments from this code review:
## Overall Comments
- Consider renaming the WithTimeout option to something like WithKeepAlive or WithKeepAliveTimeout so its purpose is clearer and doesn’t clash with other timeout configurations.
- The keep-alive loop and its tests use real time.Sleep, which can slow down and destabilize test runs; consider injecting a clock or timer interface to make the logic more testable and deterministic.
- startKeepAlive ignores errors from c.Send on ping (using nolint); it would be safer to handle or log these errors so ping failures don’t go completely unnoticed.

## Individual Comments

### Comment 1
<location> `ext/sse/server_test.go:353` </location>
<code_context>
 	})
+
+	t.Run("timeout", func(t *testing.T) {
+		srv := New(WithTimeout(3 * time.Second))
+		rw := httptest.NewRecorder()
+
+		_, _, _, err := srv.Join("keepalive", rw)
+		require.NoError(t, err)
+
+		sm := &streamerMock{
</code_context>

<issue_to_address>
Missing test for WithTimeout(0) and negative values.

Add tests for WithTimeout(0) and negative values to confirm the keep-alive routine does not start and clients are not timed out unexpectedly.
</issue_to_address>

Please address the comments from this code review:
## Overall Comments
- Replace time.Sleep-based tests with a controllable clock or shorter intervals to avoid fragile or slow CI runs.
- Ensure that concurrent pings sent by startHealthCheck via c.Send won’t race on the Streamer/ResponseWriter, e.g. by serializing writes or flushes.
- Rename the WithClientTimeout option (or update docs) so its name matches the description (e.g. WithTimeout) for consistency.

## Individual Comments

### Comment 1
<location> `ext/sse/server_test.go:374` </location>
<code_context>
+		require.Equal(t, body, ": ping\n\n\n")
+		time.Sleep(2 * time.Second)
+
+		err = context.Cause(c.Context())
+
+		require.ErrorIs(t, err, ErrClientTimeout)
+
+	})
</code_context>

<issue_to_address>
Suggestion: Add a test for client activity resetting the timeout.

Please add a test where the client receives an event just before the timeout to confirm lastSeen is updated and the client remains connected, validating the keepalive logic.
</issue_to_address>