Kirk's reaction to La'an's name was strong enough that I feel like it's a misdirect. They want us to think she dies to maximise the drama when she narrowly escapes whatever they have planned for her.

The show definitely wants us to consider it a possibility that the reason La'An isn't on the Enterprise in TOS is because she died. However, we also don't know why Una isn't on the Enterprise in TOS. For Una, I'd consider the most likely explanation to be that she got promoted and now commands her own ship. In such a scenario, it could just as easily be that she took La'An with her as her first officer. In that case, Kirk being sad at the mention of La'An's name could be that they broke up and he took it badly. But we just don't know.

I do consider it to be quite likely that they'll stick with Ortegas leaving to become a flight instructor, especially as that was shown to be the case BEFORE Future Uhura's time displacement.