Right here we go! OP you could have been me a year ago. The work situation and your DD's personality. My DD is the same age and started school a few weeks ago, fingers massively crossed she is sleeping the best she has slept for 14 months at the mo. She stopped sleeping last summer, when we changed from nursery and preschool. I think it was kicked off by anxiety, but then became a body clock mega habit that she actually couldn't do much about. One difference is that she would go to bed ok, but at 1:30 pretty precisely she'd wake up and be awake for at least an hour and a half, and then wake again at 5 for the day. She was an overtired mess and her behaviour really suffered. The sleep deprivation was so so hard. So you have my full sympathy.
My main suggestion is to look up 'bedtime tokens' and try that. The way it works is this. Sit down with your DD and have a family meeting about the importance of sleep, explain the bedtime tokens. Get some nice card, stickers and pens and a pot and get your DD involved in making a set of bed time tokens. At first, make loads, more than you need. When your DD goes to bed, any time she gets out of bed or calls you in, that's fine, but it costs a token. She can use as many tokens as she likes, she's in control. If she has any tokens left in the morning, then she gets a treat. She can choose her treats. My DD chose maoam type sweets, so if she had tokens left in the morning, she had a sweet. No tokens, no sweet. After a few days, you gradually start to reduce the number of tokens available. Your DD is in the driving seat, so you say something like you're doing really well, I think you only need X tokens now! Eventually you get it down to say 3 tokens, and after a long time you forget about it entirely.
To give you an idea of how this worked for us, we started off with 50 tokens and used 33 the first night. We quickly got down to 6, within a few weeks, then got stuck on 6 and had to reincentivise with some better sweets to get down to 3. Then they just gradually got forgotten about, but DD still asked about a sweet. Eventually she forgot about the sweets. This process has taken a full year. But it got significantly better very quickly.
I heard about this method from a sleep consultant who we used, sleepy moonkeeper. However, I researched it myself and found some science based write ups about it. It really worked for us but I still feel DD's sleep is heavily managed and she's only just started to sleep through for more than a couple of nights on the trot. She's at a Personal Best at the mo of 11 nights.