I'm considering a campaign set around the time Thassilon was founded, so I've been thinking about the original 7 runelords. As a Thassilonian Enchantment Specialist, Sorshen would want to periodically check on her enchantments to make sure her ensorcelled minions weren't faking. In a similar vein, I would expect her to want updates on the status of Golarion while she waited in the Eye of Desire.
As to whether Sorshen was fully conscious or slumbering-but-semi-conscious, my take is that it is a combination of both but leaning heavily towards semi-conscious--just aware enough to receive news updates and consider what they mean for her plans and update her plans accordingly while not losing a wink of her beauty sleep.
One thing to remember about Sorshen is that she is the genius who reverse-engineered and improved upon the Everdawn Pool to create runewells. She set the standard for runewells, and--in accordance to Xin's benevolent vision--shared the design for runewells with her peers, something she later regretted per Secrets of Roderic's Cove. Xanderghul, the other runelord who governed from Xin's original appointments until Earthfall, created a runewell, but his pride wouldn't let him ride out the aftermath of Earthfall in something someone else designed, so it's unlikely that he would have made the effort to improve upon it. Karzoug, Alaznist, and Belimarius were the final runelords of their Thassilonian specialties, so they didn't have much time to try to improve Sorshen's design; the Return of the Runelords Timeline shows that Alaznist completed hers 17 years before Earthfall, so Karzoug probably had about the same amount of time, and Belimarius had to rush the job working from Karzoug's intentionally erroneous "Runewells for Dummies" handbook.
What I'm getting at here is that, while the other runelords had the "standard" runewell design, Sorshen had 1,159 years to upgrade the Eye of Desire. Whereas the other runelords had the runewell equivalent of the cave-built MCU Iron Man armor, she likely upgraded the Eye of Desire to the equivalent of the nanotech MCU Iron Man armor. Her Eye of Desire probably had secondary alarms to wake her up periodically (every century? every millenia?) even if the master alarm hadn't activated yet so she can get up and stretch her legs and double-check that nothing's amiss before going back to sleep. It likely had communications inputs to get news from her vampiric followers and probably had scrying features as well. The Eye of Desire probably enabled Sorshen to remain asleep but enter a state of semi-consciousness whenever news updates came in so that she could consider what they meant for her plans and update her plans accordingly. Over the millenia, that level of awareness gave her the time to reflect upon her life. Coupled with what she found when she emerged after Karzoug (and probably Ileosa) was defeated, that was enough for her to decide that she was done with Evil (but she's not ready to be Good--at least not yet. Ten thousand years from now...who knows?).
Askar Avari, that's an interesting take on her time inside the Eye of Desire. However, I'm not a fan of horror, so I'll be going with what I said above. Plus, I would expect that the immortality that we see in the game comes with the mental/emotional tolerance to deal with the passage of thousands, millions, billions, trillions, etc. of years without any problems unless Something Goes Very Wrong or The Plot/Storyline Demands It or both.
