It's OK, that's solvable. So, three important things here:
(1) Never, ever leave until she's ready for you to
She must trust that she will always get as much support as she needs to go to sleep. If she suspects you will sneak out before she is ready, she will deliberately try to stay awake in order to make sure you will stay. If every time she relaxes and starts closing her eyes, you go. She'll not allow herself to relax in order to keep you there.
You need to build her trust that you'll never do this, then she can relax straight away when she gets in bed, safe in the knowledge that she can go to sleep and you wont leave her just as she's getting comfortable.
Always stay until she has been fully asleep for a good 10 minutes.
(2) Clear and non-negotiable expectations that she must lie still and be quiet at bedtime.
Her "babbles, cries, fidgets about" needs to be not acceptable. Have a mantra you say that sets out very clearly what you expect. For example "Sleep time now, we lie still and quietly to sleep". This makes it clear to her what is expected - that it's bedtime, that she must lie down (and that sitting up or moving around is not what is expected) and she must be quiet (so babbling and crying is not what is expected).
Constantly reaffirm this. Have high expectations of her behaviour. So pick her up on it if she babbles or fidgets with a firm "NO... No, it is sleep time now, we lie still and quietly for sleep. Nan night"
It helps if you have similar high expectations of her behaviour generally and clear boundaries, as with all toddlers
(3) As soon as she is comfortable with what you are doing, withdraw slightly in a very consistent way
This is the important bit, that allows you to make progress towards her sleeping independently.
Currently you are sitting next to her bed and facing away, not talking or engaging. Id change that and start off facing her so that you can engage using the mantra statement if she does not lie quietly or still. This needs you to engage with her, but in a repetitive and firm way, and without any conversation.
I'd start off standing by the cot. Have a kind and compassionate composure, not combative or negative, you're here to help her but she must follow your rules. Repeat the expectations at every 'transgression'. Stay all the time until she's fully asleep, standing quietly by the bed.
Do that for as many nights as it takes to develop the trust that you wont leave too soon. The first step needs her to stop fighting to stay awake, she does that by trusting you'll stay. I don't know how long this will take, if she's constantly expecting you to leave her it might take a while to trust you wont. While developing that trust you are also building your very immovable boundaries of expectations - constantly and consistently reaffirming that you need her to be still and quiet.
Once that trust is built, and once she accepts the boundaries that she must lie quietly and still at bedtime, she should start going to sleep more quickly. Through all thro all this stay standing by her bed, facing her, as she goes to sleep and for a good 10 mins after being asleep. Never be tempted to leave earlier or you'll destroy the trust.
Then, once she is settled in this, withdraw slightly. So this may mean that you stand facing her (so you can engage with the mantra if needed) but a step away from the cot. Do that for as many nights as is needed for her to feel OK with it. It might be 2 or 3 nights, it might be a week. Still stay until fully asleep.
Next, once settled with you a step away from the bed, withdraw slightly again. Stand by the doorway, but still facing her (so you can repeat the mantra to lie still and quiet, if needed). Again, wait until fully asleep before going. Again, do that for as many nights as is needed for her to feel OK with it. It might be 3-7 nights.
Then keep on withdrawing every few days, once she's OK with the previous stage. So have a few days standing just outside the doorway. Have a few days where you "just pop to the toilet, promise I'll come straight back". Keep your promise, and be super quick. Tell her what you're doing, reassure her your back and then carry on waiting until asleep. Do this over several days, the same one quick trip away from the door but develop the trust that youll come back.
Next Have an upstairs job to do that means you can keep popping back to the door. So settle her and wait by the door to make sure she's settled. Tell her you're putting washing away, that you promise to stay upstairs and will keep looking in on her. Keep your promise. Look in on her frequently at first, every minute or two. Give her a gentle compliment each time so she knows you came back "good girl, I'm still here, be back again in a minute". So back four, five as many times as it takes until she's asleep. But keep coming and going from the door, being a reassuring presence until she's fully asleep.
Last steps Once she's fine with you coming and going from her doorway, make a promise to her that you'll always stay upstairs and wont leave her until she's asleep. Continue with your evening upstairs job (putting washing away, tidying up, whatever) and pop back to her door less and less frequently over time. Eventually to the point where you put her down and she trusts that you're there for her upstairs but she can be asleep in her room on her own.
I forgot to mention keeping the door ajar through all of this, make it so she can see or hear your comings and goings upstairs, or call to you if she needs you, reassured you're there. The idea is to gradually teach her that she can still have your reassurance without you being there.
Its a long process, but it is solvable. Good luck!