What does the dragon want?

[KorvinStarmast]

Just out of curiosity, is it on Soefra or Noefra? (Sounds like Soefra based on the time bubbles).

Spoiler: Problem definition spoilery

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2. The party has evidence that the dragon has bonded with the spirit of the mountain it's on, extending its lifespan and supercharging its powers (granting it semi-druidic-style nature/elemental aspects) but also restricting its range (much like a dryad and its tree) and making it semi-fey-aligned.
3. The party is soon going to climb the mountain and meet with the dragon.
4. The party is level 7, made up of a rogue (swashbuckler/pirate), a druid (acolyte/moon), a wizard (fisherman/illusionist), and a paladin (sage/vengeance).
5. The party has access to a self-propelled ship (the area being on the shore of a large bay).

- It is also very tired of life. When it dies, it will likely ascend as either an elemental entity or as a minor Ascendant (pseudo-god).
- It hasn't seen or interacted with mortals in (~4-5k years).
- The mountain spirit ... It's only being held together by the bond with the dragon and the dragon's own spirit/will.

Setting facts:

There are larger groups of them on the other side of the continent as well as many, many more on a different continent altogether.

OK, Soefra is still my guess.

why the dragon called them over.
Other than 'bed sores' I'll suggest that the recent time quakes caused by the various bubbles bursting (What bubble? We never saw no bubble!) didn't just wake it up; the time tremors changed the nature of the dragons dreams which had, for a few millenia, been where it spent the most of its time. Time heals wounds, but this time tremor has re opened the wound and profoundly disturbed the dragon's dreams, and it won't go away.

Why the PCs have been called upon? Something was left undone and the dragon wants to resolve it before dying
What was left undone?

Spoiler: Nested reasons in this suggestion

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Given your time frame, I think that Ygraine or someone in her elf community (who are from a similar "a few thousand years ago") had made a bargain or pact with this dragon to protect that area. (A bit of Fey/Elf connection here). That's why it is sedentary, but, as a part of that dialogue and relationship building, a long time ago an elf/gwerin {pick a class} formed a powerful bond with this dragon's offspring (one of them?) and they went off on various exploits of derring-do. Their deeds passed into legend (and informed the creation of the Dragon Riders in Soefra) but while off on an adventure/quest the pair suddenly disappeared
(1) Headed to another plane and ended up remaining there? or
(2) Wandered into a time bubble and got moved forward or back in time)
(3) Were caught by an evil doer and held in suspended animation (per the spell) and are still in suspended animation.

Twist: the petrified dragon egg is the sleeping / dreaming dragon's grandchild.

The first desire Dragon as Mountain seeks is, before dying, to reconcile with my child. Apparently, running off with that elf caused some friction between parent and child. "You ran off, and you never presented me with any grandchildren!" "Mom, get off my back" or something like that. Dragon now regrets the estrangement between self and child, and because of the time tremors, the immediacy of that conflict is now very current. Time heals wounds, but this time tremor has re opened the wound.

A second desire: affirm its family legacy before it leaves the mortal plane. (But wait, there is one!) This may include side quest to revitalize the petrified dragon egg, or, free the child from the suspended animation or both.

Third desire: good stewardship and honor. During this conversation the party should receive hints that they need to warn various folk nearby (to include the goblins) that the spirit is soon to leave/change, and work on a disaster plan, or an evacuation plan, since the dragon's death will leave an unstable area behind it. (Something like "I've protected this valley for so long, nobody will protect you once I am gone" or "find someone to protect it when I am gone" are both was to get the party to go and find some fey / dragon / druid NPC somewhere who will take over from the dragon when it finally breaths its last. Dragon feels honor bound to provide for continuity.

I 'll throw in a few other ideas later, but I think that this will be a good motive that ties to the strangeness of time in Soefra that you have already established.