These encounter ideas are bulked out using repeated firings of the Bellard tool with some minor sense-checking and clean up:
What are these prideful, domineering arcano-technic time-wanderers up to?
1. Snacking on a previous group much like yours who stumbled in on them yesterday.
2. Off mission and have gone rogue, terrorising the locailty with plans to set up a petty kingdom.
3. Setting up a forward operating base for a long-play. They are currently quietly laying the foundations for a settlement that will arrive when the local invertebrates complete their (slightly forced) evolution.
4. Conducting a survey to identify a piece of terrain that will survive through the next million years so they can bury a cache that will be needed then. There is a massive disagreement between the senior surveyors over the calibration of their measurements - either this continent or the next one over will be subsumed into the oceans in mere hundreds of thousands of years.
5. Tending a ship nursery, all is quiet just now and the guardian beasts are dormant, but this is the place where they grow the world-ending horrors to unleash on other places.
6. Trying to restore a facility. They are heavily armed and extremely jumpy because they don't know what took out the last crew but it was clearly dangerous as it left no traces.
7. Having a coordination meeting, as they attempt to puppeteer a war in the region. Unfortunately one of the elders had gotten trigger happy and the others are trying to stop them setting off the plan early.
8. Just completed the takeover of the last of the royal houses on this seaboard. They have left their puppets in place and are now coordinating with other planes to see what resources they need to send where.
9. Developing a new archano-technic wonder weapon. It does not work but their leader refuses to admit that and the rest of the group is growing increasingly frustrated.
10. Trying to engineer the driving off of a dragon who has laired on top of a cache of deep-time resources. They cannot start their continental conquest until they drive the dragon off but the locals are mostly lizardfolk and dragonkin who quite like Grandfather up on the mountain.
11. Coming to investigate who you are now that you have stumbled into the early-warning zones of their well run stronghold; a troupe of thralls is about to make contact to pin you down until their superiors can get here
12. Sealing away an old fortress for the next few aeons in accordance with their long-range scrying. This is the last of the moth-balling group, lead by the stronghold commander who will set the arcane wards as they leave.
13. Growing a thrall army and sealing it away for a war in the future. Strangely this vault seems very far inland for the aquatic thralls that you find in the pods.
14. Engaging in a long-range planetary engineering by helping elves crush the local dwarf and fire-giant clans and snuff out the glimmers of local human civilization. The prophecied expansions of the great forests will eventually induce an ice age and allow raiding of currently sub-aquatic riches while the seas are low
15. Growing a world-tree, eventually to blot out the sun and allow their rule beneath its shade.
16. Trying to find the leader of their group who puppeteered one of their warbeasts and opened the pen. They are trying to figure out how to round up their deadliest works without losing too many of their minions. A significant faction would cry no tears if the leader was lost during this incident.
17. Prophecy has revealed a near term doom coming to this location and the group has fallen into vicious fighting over the few spaces remaining on their interdimensional bastion. The gloves are off, these flayers have gone competely feral on each other.
18. Has an artefact of immense power, currently recharging after devastating the last planet, and are in a mild panic about how to hide or defend it if anyone turns up. They are trying to figure out the minimum amount of resistance they could put up so that intruders would 'steal it' and then they could wait for it to recharge and steal it back closer to when it is useful again.
19. Actually working hard to save this entire system from a cosmic natural disaster. In saving their own skins, they will also save most sentient life on this world and three others.
20. Catastrophically successful in their war-breeding program, the latest generation of kaiju-scale warbeast is three times larger than they planned and they are debating what to do with it when they run out of sedatives.
21. Conducting a continental scale survey because leader A has a plan to crack this planet but leader B insists that their favourite mountain range is preserved.
22. Dropped their planet-coring weapon that was meant to go through a dimensional rift which is now boring its way to the core off-schedule. The bad timing and planning means it will do no more than trigger a new volcano at this location but they are now trying to pack up their labs, library and stuff and get transport elsewhere in a hurry.
23. In the last stages of dying slowly after failing to find a cure to a bio-weapon from two epochs ago. Most of their time is being wasted on re-fighting that war and analysing what went wrong instead of finding a cure.
24. Searching for a fugitive who is has possessed a bio-ship and is hiding in their shipyards. This involves waking up and flying around in all of their dormant fleet to figure out which one is not acting ship-like.