CoC2's sleep is pretty weird. It seems to be in a midpoint between CoC's sleep and TiTS's sleep, in that you can start it at any time like that of TiTS, but it will always deposit you at the same time like CoC. I do not like this. In CoC, it makes sense to have sleep function as it does because of the game's mechanics. Sleep is the full heal you have after a full day of exploring, encountering foes and trekking through dungeons. You always return to your camp after a random encounter, the world literally bending just to keep your journeys consistent in their times. It's where you sleep, where you store and use items, where your followers go. It's the home base, and there's a lot to be doing all day while there is a guarantee that you will be back in time for bed. So, it makes sense to restrict sleeping so it is only accessible at after a certain start time, and it makes sense to have it end at the start of a new day.
In TiTS, your ship serves most of the same roles as the camp. You have item storage, you have followers/crewmembers who sit there, you have your bed, you have a hub menu that takes you to different areas which can host random or set encounters. There is, however, a crucial difference: You don't return to your ship after every random encounter. You don't need to be there to use items like transformatives or consumables, or to equip your weapons and armor. In CoC, the camp is where you return to all the time, but in TiTS, you only return to your ship when you need it. If you need to sleep, whether for soreness, for healing, for energy restoration, for levelling up, or just to pass the time. If you want to interact with crewmates, masturbate, store items, or travel to another planet. The ship is a hub, but only one you return to when you need to, not all the time. So, because you're not on a super-strict time schedule in TiTS (and also because there's healers on many planets that don't need you to sleep, and resting a few hours is good for restoring energy), it makes sense to have Sleep be a loose thing, where you can do it whenever and it just lasts a few hours. It's a utility, a tool you use when you need it rather than an endpoint to each day and a fresh start for the next.
To me, it seems that CoC2's sleep wants to be CoC's sleep, but the game it is built into is much more like TiTS. Even ignoring all the weirdness with what makes the champ autosleep (The trainings are extremely fucked, as I said two pages ago, and I'm amazed that masturbation still hasn't been changed to allow the champ to stay awake after flicking their nipples or stroking their cock), we can see why I say that CoC2 wants to have CoC's sleep: The first and most obvious is that it has set times. You will always wake up at 8 (well, the actual time you wake up seems to be randomized to be between and including 8 and 8:14), and if you go to sleep or masturbate after 6 you instead wake up 26 hours later at the 8 am the next day. The second is that most npcs in Hawkethorne stop working after a certain time. I think they go to sleep a bit too early since it prevents you from selling stuff off and turning in some quests (and also blocks training), but it's logical that they sleep, helps instill the idea of a living world (even if it's annoying), and it does incentivize just going to sleep since your interactions are limited. The third is that the level three perks only activate on sleep. I have my own niggles with these, namely that they do very little and only last for such a short time that by the time I get into any encounters they've usually worn off or will wear off by the next (as such I kinda just want their timers to be extended), and also since the shopkeeps disappear at night that means that the time for shopping is the morning and midday, which is also when the buff is active, but still, you can see that the perks incentivize going to sleep after they wear off to reapply them.
So, what about the game being structured like TiTS? As it is in TiTS, you don't return to the Frost Hound after every random encounter, you only return after a long time of adventuring. If it weren't for Kiyoko, I would not pay attention to the time, or when to sleep. There are several ways to heal, both through npc interactions like Sander or Cait, or through combat powers like Heal or Eternal Light, so this goes even further than TiTS by making you not even need to return to a civilization to heal. In terms of exploration, every tile takes like 40 minutes to travel, and you're traveling through a lot of tiles. It's fewer tiles than TiTS, but I think each movement represents much more time than in TiTS too, so a lot of time is passing. You're not guaranteed to be back at Hawkethorne in time to sleep, unless you're budgeting the time out so you get back at 5:30 (like I do, because of Kiyoko). Since sleeping to heal really just is not needed, and since the buffs have such small effects that I literally can not notice how they help in combat, and since consumables can be used and items can be equipped at any time, there's little need to return to the inn or to set up camp. As a result of this, sleep should be a tool to level up and be an alternative tool for healing, but instead of having it just be a set amount of time like TiTS, it has a set endpoint and a maximum start point. The game mechanics are better suited for a TiTS sleep, but the player is expected to sleep at a set time like CoC.
The only reason I sleep, aside from leveling up, is because of Kiyoko. When it comes to her, however, she doesn't really benefit from the CoC2 style sleep. She doesn't have a set interaction time, she just appears whenever you sleep, so if you want to interact with her prior to freeing her, you're either going to put it off until after some time adventuring, or you're going to binge-sleep. Because I don't like the idea of wasting so much in-universe time on one sleep interaction, when the value for in-universe time could go up by adventuring until 5:30 in the morning and then sleeping all this leads to is 2 hour sleeps, every single day. If it's a TiTS sleep, then I wouldn't feel as pressed about constantly making sure I'm back by then, and instead just focus on actually experiencing the game, adventuring, and sometimes using the sleep function. It really seems inconsequential, but the set sleep times combining with Kiyoko's sleep visiting makes the game feel actively worse, because I feel like I have to constantly maximize how much time I use on interactions, events, and encounters each day rather than just having fun. It makes me want to optimize the fun out of the experience, just so that I don't waste time. This would not happen if CoC2's sleep had the same mechanics as TiTS's sleep.