Why did the Engineer stay in stasis instead of taking off?

[BlueMarsalis79]

It is the exact same scream just distorted, being that Neomorphs and Deacons share many features, it probably shared their characteristics whatever it used to be.

[thexenomorph]

Actually despite or in addition to what I posted previously, you can hear the Deacon scream as the holograms activate.

That is soo freaky! I'm guessing an adult Deacon!!

[Local Trouble]

I wonder what happened to its body.

[SM]

Remember all those mountains?

[OpenMaw]

Remember all those mountains?

And it starts singing some John Denver.

[SM]

It all ties together.

[xenosemen]

We see three other pods around the dais as well, all with conspicuous holes punched in them around the chest/upper body area. My theory is that all four crew attempted to enter stasis as a means to escape the outbreak, which was already taking place. Three of them must have been infected before going in though, and either "burst" or gave birth to something while in the pods, perhaps years or centuries afterward, due to the slowing down of their metabolisms. Our boy was just lucky enough not to have been infected before he went into stasis.

It would explain why he wasn't woken after a pre-set time as well, either as an automated safety mechanism, or deliberately. You couldn't be sure what you'd wake up to, so safer to remain dormant indefinitely and hope that someone came to investigate and revive you once the outbreak was contained. For whatever reason, it seems nobody came, and even then the prospect of dying unconscious in stasis after thousands of years would have to be preferable to the alternative.

As for what the engineers in the hologram were running from, while it's tempting to believe that it might be a creature or creatures of some sort, I think it's more likely to have just been a cloud of airborne pathogen, like we see in Covenant. It seems that exposure to higher concentrations results in explosive mutations that kill the target within moments (like the decapitated head), while smaller doses result in a more gradual change, even into semi-sustainable organisms (think Fifield and whatever metamorphosis Holloway was undergoing).

Whether they're running from a creature or something airborn I believe that this is the most correct answer, and quite discernable from the visual clues and other implied info given in the film proper.

[Local Trouble]

Remember all those mountains?

And it starts singing some John Denver.