Same thing happened for me. For the 3 previous stabilizer quests they autocompleted just fine when I got them, because I already collected the stabilizers before getting the quests. But for the Myterious Box quest I had collected the crystals, but not opened the box yet by the time I got the actual quest for it. The quest has ticked off Go to Archaic Mine Island and Open the Box as completed, but the tasks for finding the crystals are uncompleted and going back to the npc just results in "I haven't finished the tasks yet" despite having the stabilizer in my inventory.

I ended up ignoring the uncompleted quest and just placing my last stabilizer in the generator, which triggered a new quest to appear (Still a Keeper?), so it doesn't appear to break the game completely as you can still progress with the main goal of the game at least.

Edit: Okay it does appear to block you from getting any potential new quests from npcs if you decide to keep playing after finishing the game (main goal). But aside from that everything is completeable and all achievements are achievable.

Indeed, the "Mysterious Island" mission won't take into account the Blue Magnetic Crystal, if we find it and place it on the chest in Archaic Mine Island, before the mission officially starts.

I visited and completed some missions around the other islands out of curiosity, before these mission were officially given to me by the NPCs...

Now, I am stuck at that point of the story.

I got all of the stabilizers and placed them in the lighthouse panels by now, but the games considers that I haven't finished "Mysterious Island" mission on Archaic Mine Island, and won't let me tak again to the NPC Duari Hwara about it.

Since I can't find the mental energy to erase all of the data and start the game all over again, unless the bug is fixed soon, I'll probably uninstall for now.

For me it was also bugged, but you can still get it. just go to the Vulcano Island and fill in the 2 buckets with trash. The door will open and then the stabilizers will appear.