Sounds like she needs some compassion, unlike what the majority of the nobs here are suggesting; a harsh hand wont help this.
She's 16 an age that is difficult anyway, she's gay, which much have been hard to struggle with and likely still is and she has had an obviously difficult breakup with someone that she can relate to for (likely) the first time.
Now she's stuck at home with her parents who are on her case when she's trying to deal with a lot of other pressures and it sounds like her only release is socialising with her friends, again, understandably.
Empathise with her, sit down with your partner and discuss how you mean to go on in the future, incentivise her finding a job/course and let her know you're there to support her.
Treating her like a naughty teen will label her and will likely cause her to enable a self-fulfilling prophecy and she will become one.
I was going to say this ^
Being a 16 year old girl is hard, especially when you have set out your life choice (collage) based on your relationship, which has now broken up...let alone being gay on top of that! It was probably her first 'real' love/relationship
Chances are she knows she has screwed up and she is well on the self pity train. The last thing she needs at the moment is the 2 of you getting on her back.
However, I understand that you cant afford to support her, and all we see (as adults) is a petulant teenager who cba doing anything.
I do think the best advise really is to get her mum - not you Op, no offence, I will explain in a mo - to sit down with her and talk to her. Not in her bedroom, which is her space, or even in the house, where she could feel like she is getting ganged up on, but somewhere neutral. Get them to go and get a coffee, or go for a walk or something. Nothing heavy duty.
She loves her mum (us girls do), even if they argue and flight, and ultimately when we have done something stupid or we have split up from someone, we want our mum to give us a hug and tell us that it will be okay and it will all work its self out.
I am not saying they go out, hug it out and avoid the issue. But opening with that will help a lot. LISTEN to her, let her talk and don't judge. Once you have got this, then you can ask her what SHE wants to do with her life.
The reason why I said not you Op, cause regardless of how long you have been in her life, you will never replace a girls mum. I know and understand this being a (sort of) step parent myself. I would love my step child to confide in me and want to speak to me when she gets bigger, but I know that she will always want her mum. She is only little (5) now, but if I am around when she is bigger then I would be blessed if she chooses to come to speak to me about anything, over her parents.
Does she have any hobbies - does she like art, music, fashion, animals etc - and if she does, is there a collage course she might be interested in taking which supports that? If she does, then that could lead to her taking a Saturday job so she can buy any materials or anything that she would need to do get through collage.
Ultimately you need to speak to her and treat her like an adult, but also try and remember what you were like at 16 and respect her.