The current arrangement makes sense to me.

You get very hungry, then you reach the point where you're starving. "Starved" would mean dead, so when you're almost dead, you're "almost starved". So you go from "starving" to being "almost starved".

Objectively it makes sense but thematically the "almost starved" message simply doesn't look as urgent as "starving". A rewording would help emphasise the meaning, especially to new players.

"dying of starvation"? Would look very urgent, especially in red font

I agree - almost starved, though technically a more dire case, is less urgent than starving.

Especially with how long it takes to actually waste away from starvation - years!

The problem with using "dying" just on its own is that it's not really that intuitive on it's own - a player might look at that and think "oh damn, what am I dying of?!" And technically a player could be 'dying' from poison/sickness/old age/bleeding or a variety of other non-food related things.

Unless 'dying' is a status modifier that is added in addition to the starving status? So you would have

Starving
Dying

both in your side toolbar looking like that? So any status effects you have that are putting you close to death like poison or sickness could giving you the 'dying' status as well.

Dying wouldn't work unless it's imminent - which in JADE, it isn't. Perhaps "Starving" -> "Wasting Away"?

it's the same problem with Malnourished , as you suggested. That's more of a long-term state you can be in, even if you eat regularly.

Someone who only eats cheetos can be overfed *and* malnourished, for instance.

How about; Hungry->Ravenous->Famished->Starving

sounds good :)
Only Ravenous has some extra meanings which are not really useful, the same as with a word like 'drooling'. I would be OK with 'very hungry' instead, so:
Hungry - Very hungry - Famished - Starving