Try getting more sensory oriented toys. This doesn't mean your DD has special needs at all. But most kids at this age are very sensory led when it comes to play.
I can recommend:
Nina Ballerina magnetic dress-up doll by Melissa and Doug
Kinetic sand
Melissa and Doug pattern blocks and board
Pop-Up Pirates game (this is a 'cause and effect' game which is always thrilling for kids)
Bristle blocks
Paint with water/magic painting
The other item I think every 3-6 year old should have is a LeapPad (get them second-hand on eBay- along with some games, Letter Factory is the best). LeapPads are totally educational, entertaining, engaging. It's not a screen in the way that playing on the phone is.
She's too young to be left alone in the mornings- not because it's a danger but she does need your parenting and your input. You're not well and I can totally imagine how fatigued you are. You don't have to be The Entertainer, but just get up with her, greet the morning with her, be part of her start to the day- this is really psychologically important. It can be a snuggle in bed or even just sit her on the sofa while you get her breakfast, chatting to her. She needs you in the morning. I was a single parent to DC1 until he was 7. The important thing to focus on is ensuring that she doesn't feel alone and left to it. Again, this doesn't mean you have to dress up as Coco the Clown and entertain. Not at all. But just be there, in her orbit, in her space. I'm not a big talker in the morning but kids just need to know that you are there. They don't need all the bells and whistles, just the comfort of your presence is enough- you shuffling around getting a cup of tea with some nice music on- is comforting.
Sometimes I just leave games and stuff on the kitchen table so that when DC3 wakes up, he sees, for example, a dress up fireman on the table and starts playing with that. None of my kids liked staying in their room in the morning. They tend to want to be near mum, kids do.
Is your DD at school?