Hi OP
In the nicest possible way, you need to stop worrying about being non-confrontational or controlling.
HER behaviour is very controlling - won't work a regular job because she likes to be 'flexible', doesn't want to 'lose her identity', but won't sit down to discuss budgeting because she's 'worried what it might lead to'.
The only possible outcome of a spending review that she could be worried about is that she would need to reduce her spending.
But it's obvious that that must happen.
She is behaving totally selfishly, OP, and you need to put your foot down.
Set up a new account for just you, have your salary paid into that, pay all of the standing charges from that.
Use the joint account purely for house expenses, ie food, basic toiletries and household supplies.
Any purchases needed for the DC to be discussed and agreed in advance.
And she can open her own account, and you can pay in a discretionary amount for her incidentals (coffee with a friend, an occasional Vinted purchase), say £50-100 per month. If she wants any more personal money she can fund it herself - pushing her freelancing again, or getting a job.
If she is not willing to accept this, then I think you need to consider your future.
You are not a couple with a joint vision, pulling together, you are out on your own trying to pull a dead weight up a hill...
How do YOU feel about separating?