Past time I elaborated on this. From what I know, having oceans is kind of necessary for Earth-style plate tectonics, so a planet with no oceans would lack continental drift; without continental drift, I doubt climate changes would occur at the same rate they do on Earth
Seas are necessary indeed. The surface water acts as lubricant for the plates. Once it's gone the planet's just going to have lid tectonics with volcanoes popping up like pimples, at least until all the heat is gone. It's what Io, Venus and Mars do. Technically, without plates, I don't even think a planet can have geological "continents" made of granite and oceans lined with basalt! Though I dunno.
And a habitable planet without plates may experience inconsistent volcanism. The climate will probably be just as inconsistent in changing if it ever does. Though with inconsistent volcanism, the atmosphere could be scrubbed of carbon dioxide a lot more thoroughly, leading to freezeouts until the place turns into, in Ausaril's case for example, a bigger version of Mars or some other icy shithole.
The first implication I thought of, and the one I've considered most, would be the fact that such environments are not conducive to the formation of fossil fuels due to how dry they are. As such, fossil fuels would likely form either not at all, or in very limited quantities; if Ausaril were such a planet, it would have a significant impact on the development of ausar technology as they would be unable to achieve a human-like Industrial Revolution. (This would, at the same time, also prevent an equivalent to modern human activity-induced rapid climate change.)
No global warming (or heating or boiling or frying, pick your metaphor) for Ausaril then. I expect in their case excess heat would probably roast them before they could even realize they were adding to the GHG layer, since the endless land has no thermal inertia. But no cheap energy either, at least not as we know it.
The only solution I could think of would be for them to instead discover uranium, skipping coal/petrol power and going straight to nuclear power. After some research into the history of uranium ores, I believe that the discovery of uranium in sufficient quantities for this would indeed be possible because a) there are sources of uranium ores that don't require non-desert environments and b) of the sources that do require water, at least some of them are possible with groundwater; I think it's reasonable to assume Ausaril has groundwater as real-life deserts also have it.
An inventive solution! And the ausars themselves are full of water and water derivatives, if the wetness of Anno's pussy is representative of anything, so the water is indeed presumably underground just like in Sol System deserts.
After this, the main problems would be figuring out how to 1. refine U-235, Pu-239 and/or Pu-241 from the ores and 2. extract energy from them i.e. make nuclear reactors, both using only pre-Industrial-equivalent tech, then 3. getting enough water for the reactors to work. IMO, 3. is actually the least of these hurdles as Ausaril still has water, and the reactors are a closed system in that regard and thus don't require a constant supply of the stuff. I'm not sure how possible 1. and 2. are, though. The second implication is that since fossil fuels can't be formed, then perhaps some other types of fossilisation are also impossible. However, given how many types of fossilisation there are, all this would mean is that there are fewer fossils but still enough for palaeontology to be a thing on Ausaril. On a related note, dry deserts are actually quite conducive to natural mummification, so such natural mummies would likely play a greater role in Ausari archaeology than in its Terran equivalent.
Third is that with how stable the environment is over geological timespans, mass extinction events (which are often related to massive climate changes) would be quite rare if they happen at all.
I imagine that something like the Oklo natural fission reactor could be the catalyst for the ausars learning how to build reactors; they could study that and improve on the efficiencies. Presumably, the preindustrial Ausaril environment has lots of readily available conductors and neutron moderators.
Refinement is going to be an issue, I agree. That's going to take lots of intensive labor and thought, which might be hard to get by when your planet requires you to practically mine the stuff needed to build the empires that can sustain the division of labor required for that sort of research. And even in the circumstances of ausars imitating natural reactors, that same constraint applies.
I imagine any sort of fossilization which needs a surface water body is going to be undoable, on that I am definitely in agreement. But as you say, other forms of fossils as well as mummies will gain prominence in studies of the past.
And mass extinctions would indeed be much rarer than on this geologically volatile supercontinent-cycling planet. I can't think of more than one on Earth that was triggered by an impact.