I didn’t quite understand how ため is used when it indicates something different from finality.
Here for example what is the exact nuance?
Obviously it can’t be that the village was submerged for the sake of building the dam.
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This「ため」is conjunction which means "result". It was "purpose" before the construction of the dam.
「ダムを建設するために、村は湖の底にしずむ予定である。」: In order to construct the dam, the village is going to submerge into the bottom of the lake.
And I think this 「しずんだ（しずむ）」is intransitive verb. It is not a transitive verb :「しずめた（しずめる）」.
In either case, I am not sure why it is too odd for you to think of the village "has"/"has been" submerged for the sake of building the dam.
Imagining the context, the local government asked the citizens of the village to move out of the village in order to construct the dam.
After the successful negotiation, since everybody moved out of the town and nobody had lived in the village, the dam has been built and the village has sunk.
And now you are reporting the result : 「ダムができたため、村は湖のそこにしずんだ。」
There are two main meanings/functions to ため.
One, which you already know, is the「目的のため」, used to express purpose (translating as "for the sake of", "for the purpose of", or "in order to").
The other is the 「原因・理由のため」, and which I assume you haven't come across, is used to express cause/reason (translating as "because of" or "owing to"). This is a relatively formal construction when comparing to から or ので, which is possibly why you haven't come across it.
Using the second meaning, the sentence makes more sense to me, and would translate structurally to something like:
Owing to the dam being built, the village sunk to the bottom of the lake.
For further reading, these articles (in Japanese) provide good explanations and examples of correct and incorrect usages of the two ため constructions.