3 year old transition from cot to bed, fucking nightmare, please help

[roseopose]

DD is 3 in August. She has always slept awfully, never napped longer than 30 minutes, woke frequently at night, stopped napping entirely at 18 months. Didn't sleep through until she was 2. We recently put her into a toddler bed and she has been up til gone 9 every night since.
We've tried everything we can think of. She just will not stop, she never ever appears sleepy, never has done, doesn't get drowsy during a story or a cuddle, we've taken everything we can out of her room that she can play with or mess about with but she just prats about singing at top volume or climbing on the windowsills, getting under her mattress, inside her duvet cover and so on. I've tried ignoring her totally, tried lying with her and trying to soothe her off to sleep, tell her a story etc. She'll settle down then when she gets bored she'll bob back up again chatting away.
It's a fucking nightmare. We get no evening or break from her whatsoever, I spend most evenings in tears and I'm worried she isn't getting enough sleep as she's up at 7.30 every day. She is worse on nursery days, you would think she would be more tired but it seems to have the opposite effect.
I guess she could be over tired, I've tried making bedtime earlier, later, but it has zero effect. Bedtime routine has been the same (bath story milk sleep) since she was tiny and it's always been consistent.
Please does anyone have any suggestions?

Take everything out of the room except a sleeping mat and her covers (and a teddy)

Black out the window so that she cant pull it off (maybe tape paper to it - this is only for the short term)

Shut the door and hook/eye lock it from the outside (put it up high on the door so she cant ever attach it herself, and dont worry a strong adult yank will just pull it out, so it isnt a safety risk)

Do the bedtime routine at 6pm, nice story say night night and shut the door and leave her.

Only go back in if you hear something dangerous happening or there is crying for more than 10 mins. At that point, dont look her in the eye, take her back to bed, say night night and leave again. Rinse and repeat extending the crying time to max of 20 mins. Use a timer as 10 second feels like hours when they are crying

It will probably take 3 or 4 nights, but she will learn to soothe herself to sleep and that is a skill that it is worth the struggle of learning.

as Hard as it is I would say you just have to lean into this, if she isn’t tired she isn’t going to go to sleep so making bedtime earlier is just going to be frustrating as you’re up there for longer trying to make something happen which isn’t going to happen! I know as we’ve done this. Maybe stay downstairs a little longer but try and have things she can do on her own or play games that enable you to sit on the sofa?
plenty of outdoor time and exercise during the day and bags of patience for you. It’s so tough but You will eventually get evenings back

So until recently, she was in a cot so could not get out of bed, but now she is in a bed and can run around as she pleases.... correct?

@InceyWinceySpidy she was climbing out of the cot so we decided we may as well just take the bars off. I think we're going to try the silent putting back into bed X a million and see if that works.

@Restingpotato I know, I'm starting to come to terms with this, it's just so hard! Before she started climbing out of the cot she would go to sleep at 7.30/8 with little intervention from us. Hoping it's just the novelty of being able to get out of bed but I'm worried about her getting into the habit of playing until whatever time she likes and that sticking when she's older.

I know it's soul destroying. There are loads of Supernanny videos of the stay in bed technique if you need some virtual encouragement. It does work, but it takes time and a lot of effort on everyone's part.

Our twins were like this, and what made a big difference was the room being completely dark.

They will got to bed around 6.30-7pm and be asleep in ten mins with the blackout blinds and curtains. Without, I will still be in and out of their room like a yo-yo until 9pm because it's just day time to them.

They are also 3.