The lack of any real time pressure currently is what gets me most. Once I realised resting had no impact on the progress of the groups' ceramorphosis or the Druids' eternal chanting, the story lost all sense of urgency and a lot of its credibility. I can only imagine this is done purposefully for data gathering reasons. What I am hoping is that these quests with implied time pressures actually make themselves felt so that taking a long rest is a much more meaningful choice. To really make this work, the short rest system needs to be expanded. More short rests per long rest, the inclusion of hit dice and the removal of health gain from food items, allowing group interactions and story beats that currently only take place for long rests to happen during short rests where appropriate. It's about managing resources to allow you to reach your desired outcome. Right now you have nothing to manage, nothing to loose from having a good sleep, fighting some spiders for 20 minutes then popping back off to bed.
It's primarily a game. Time limits never work very well for games (or aren't liked). You cannot add time limits without making the player feel punished for exploring, even aside from the fact that it will encourage players to avoid as many fights as possible, which should not be the goal.
Rest limits are also problematic as players are different, not to mention the possible team compositions. Rest limited by objects seems not such a bad idea, but remembering how he was disliked in PoE1 I don't know if it's a good idea. The time limit is also a tragic idea as it actively encourages the player to minimize the game. It seems to me that the best idea would be to prevent a long rest in certain places, as it currently works in the witch's hideout, and also when there are enemies nearby.