尽きる: curiosity that lasted and water that ran out
Read the negation of exhausted curiosity against water actually running out before the mountain hut, preserving polarity and the stated time order.
Curiosity sustained by discoveries
旅先では珍しい発見が続き、私たちの興味は尽きることがありませんでした。 reports unusual discoveries continuing throughout the trip, so curiosity never ran out. 尽きる, read つきる, concerns exhaustion, but 尽きることがありませんでした negates it here.
私たちの興味 is the thing that did not become exhausted. Read the discoveries and the curiosity during the trip without turning the negative into a report that interest ended.
Water exhausted before arrival
山小屋に着く前に水が尽きてしまいました。 reports running out of water before reaching the mountain hut. 水が尽きてしまいました presents exhaustion of the water as an actual past result.
山小屋に着く前に places that result before arrival at the hut. It does not locate the party inside the hut when the water ran out or supply a later replenishment amount.
Negation and an actual exhausted supply
The first sentence negates exhausted curiosity, while the second reports exhausted water. The negative wording and past result matter alongside the difference between their objects.
Do not replace the contrast with a question about exact remaining quantities. The starting water supply is unstated; the core information is what ran out and its timing before arrival.
Which example reports actual exhaustion: 尽きることがありませんでした for curiosity or 尽きた for water?
Show the answer and why
The water actually ran out before arrival at the mountain hut. The discoveries continued, so the example negates exhaustion of curiosity.