Please don't blame yourself OP, you are a good mum and doing the right things
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You are clearly stressed and this is colouring your judgement.
You know the answer, you need to hold it together. I suppose you consider yourself a professional woman, you want your career and you want do the best for your DC. You know that you are capable enough to do both well. You are in this situation because you are confident and very capable woman, and there is nothing better for your DC than that.
Don't pander to the yummy mummy lobby, it's a myth, those women would give everything to have a meaningful career and financial independence. Yummy mummy also depends on good middle class income of their partners. Poverty will not make it better for your DC. stay true to your values. Any job with good income will be demanding. It is absurd to be scavenging for low paid part time jobs in the gig economy. Poverty and depression will not solve any of your current problems and will add some more. Changing jobs in the middle of stress crisis is not a good idea. You need to stabilise first.
You need to regain balance and reduce stress, by not being hard on yourself. Decide which non essential balls you are OK to drop -
Have some me time, pampering, entertainment, relaxation.
Your boys are already quite independent, soon they will be grown up. You don't need to treat them like toddlers. It is a different phase. Define what it means for you. Try to establish good work ethic and routines with them. Instead of screen time, instill a routine of useful positive activities which they pursue independently. Work on family culture and ethic in which they are self-regulating and responsible, ambitious, support you, including emotionally and with chores. Put some hard carrots and sticks, limit their devices and demand compliance with your routine. Can't they attend their clubs and friends by themselves?
Agree with them how to maximise the utility of your time together, play hard, whatever you want to do with them, make it count double.
Recruit all the support you can have, au pairs is a good idea. Do you have your parents? This is the time when you need support. I don't know what you could do about your ex paying more and doing more with them, maybe define specific things which he would be motivated to do?
Trust yourself 