This "wert sein" can take objekts in all cases. Akkusative, dative and genitive. As "wert" is combined with "sein" it is probably a predicative adjective "worthy" or maybe it was once a predicative noun "der Wert" "the worth". There is also the expression "von Wert sein." "to be of worth".
Akkusative object: expresses the worth assigned to the subject.
Das Bild ist den Preis wert. The painting is worth the price.
Genetive object: expresses if something is worthy of something, more as an idealistic than an actual worth.
Das Bild ist der Mühe wert. The painting is worthy of the effort.
The dative object is optional. It expresses the person who judges the worth or worthiness.
Das Bild ist mir den Preis wert. The painting is worth the price to me. (dative + akkusative)
Das Bild ist mir der Mühe wert. The painting is worthy of the effort to me. (dative + genetive)
Oftentimes, it is unclear if the objekt is genetive or akkusative. You can use the same words in the other case.
Das Bild ist die Mühe wert. (akkusative) The painting is worth the effort.
Das Bild ist der Mühe wert. (genetive) The painting is worthy of the effort. (seems to be genetive in English, too.)
With many wordings you can not distinguish between genetive and akkusative.
Das Bild ist viel wert. The painting is worth a lot. viel is the object although it doesn't even seem to be a proper noun. I would guess akkusativ.
"es" is a tricky one too. The actual genetive should be "seiner" or "dessen", but sometimes "es" takes over. For the original sentence I would stick with akkusative.
Die Woche ist es wert. The week is worth it. (not worthy of it.)
subject Die Woche kopula verb ist akkusative obect/pronoun es predicative wert.
It's not only a cr@p sentence, it is an ultra cr@p sentence. Totally meaningless in English.
Imagine a séminaire, or a trip to some remarkable wilderness, or a fashion or film week somewhere, or a week's spiritual retreat. It might be worth going to, or doing something of that ilk for a week.
The issue I and other English-speakers are having, is figuring out when/why you would use this sentence. For your examples, I would say, "That trip was worthwhile," or, "That trip was worth all the work I put in last week." I asked my German friend, who also teaches German, she said that it sounds as weird in German as it does in English. The sentences that sound correct to her were structured almost exactly as I did above. Maybe it's a regional thing?
Don't worry about it, die (or der, das) is sometimes translated to that.
What context? There is no context given. The sentence stands on its own and--much like many sentences offered for translation--leaves us wondering about what the larger conversation could be. However, the purpose of DuoLingo is not to tell a story but to teach German grammar and vocabulary.
If you'll read through the comments you'll see I provided a scenario where one might say "Die Woche ist es wert."
But since you're not trying to learn German "parrot-fashion", it really shouldn't matter if you can use this particular sentence as it is. Instead, use it as an example to understand how you can synthesize your own sentences, such as "Das Auto ist es wert," oder "Die Ausbildung ist es wert." The key is to recognize the structure: [etwas] ist es wert.
Das ist was die Eule hier lehrt.
In this case "wert" is a predicative adjective. The full verb would be "(etwas) wert sein". "Sein" itself is then a kopula verb that is not quite complete without a predicative. Predicatives are part of the verb and move to the end of the sentence as part of the verb bracket. You seem to alredy suspect that, so you are probably familiar with the concept of the verb bracket.
So you do understand what the sentence means: you provided an alternate way of expressing the same thought.
But with regard to your never saying it the way die Eule chose to say it, DL is not trying to provide you with a library of canned phrases that you can use to express yourself. Rather, die Eule is attempting to teach us how to "speak" (which actually means "hear/read, understand, and respond") German. Although you might not ever say Die Woche ist es wert, you might hear someone else say it, and if so, should be able to understand. There is no chance I would ever say Ich bin schwanger, but I would like to understand if my wife or daughter said it.
You're missing the point. This is a language learning environment, so why use phrases like "That week is worth it" which is not normal English? There are so much better ways of modelling the language. The point I originally made was that this type of comment is something you would make in retrospect. "Yes, it WAS a difficult week, but with hindsight, it WAS worth it". You couldn't say that until afterwards, so therefore "The week IS worth it" is meaningless.