Post-break up, advise and tips please

Two weeks before going on holiday (with my girlfriend and her mum), she asked for some space. I listened and gave it to her however this made me question whether I should go on holiday with her. I asked her multiple times and she always responded, ' Yes I really want you to come and am really excited, etc'.
So I went on holiday. Two days into the holiday we are having drinks (just us two) and she tells me she wants a break to work on her mental health.
I responded, saying I'd rather be black and white. We are dating or we aren't, offering her space and asked her what I could do to help.
She responded by saying that she needed time to think about it.
During this time I didn't know how to act, couldn't sleep and felt sick of the thought of her with another person. Days later I saw she's been messaging this guy (who I had never heard of) and asked her about him as she was constantly messaging him back and responding to the tiktoks he sent whilst not responding to mine. She got defensive saying he was just a friend.
The next day I confronted her and told her how I was feeling and needed to know that day whether or not we were dating otherwise I'd decide and break up. We talked for 30 minutes and she said we both need to work on our mental health and should break up.
I go home and delete her on social media other than snap (cause we needed to exchange stuff).
It's now been just under a month and I feel I need clarity on the break as I still think about her 24/7 and if she actually loved me or not.
I don't want to get back with her right now (maybe in the future) but I feel as if she never loved me.
Should I ask her about why we broke up or not? if so what should I send?
How can I cope with this break-up?

It sounds like you've been through a lot emotionally, and it's completely understandable that you're seeking clarity and closure.
First and foremost, please know that your feelings are valid, and it's okay to need time to process everything that has happened.
As for reaching out to your ex for closure, it's a decision only you can make. Consider whether hearing her reasons for the breakup would truly bring you the closure you're seeking, or if it might reopen wounds. If you do decide to reach out, approach the conversation with a calm and respectful demeanour. You could say something like:
"Hey [her name], I hope you're doing well. I've been reflecting on our relationship and the breakup, and I've realised that I still have some unanswered questions. I'm hoping we can have an honest conversation about why things ended the way they did, so I can find closure and move forward. Whenever you're ready to talk, I'm here."
Remember to prioritise your own well-being throughout this process. Coping with a breakup can be incredibly challenging, but it's important to give yourself permission to grieve and heal. Surround yourself with supportive friends and family, engage in activities that bring you joy, and consider seeking professional support if you're struggling to cope on your own.
It's natural to wonder whether your ex truly loved you, but try not to dwell on it too much. Ultimately, what's most important is how you feel about yourself and your own worth. You deserve love and respect, and it's okay to take the time you need to rebuild and rediscover your self-confidence.
I wish you the best of luck.

Two weeks before going on holiday (with my girlfriend and her mum), she asked for some space. I listened and gave it to her however this made me question whether I should go on holiday with her. I asked her multiple times and she always responded, ' Yes I really want you to come and am really excited, etc'.
So I went on holiday. Two days into the holiday we are having drinks (just us two) and she tells me she wants a break to work on her mental health.
I responded, saying I'd rather be black and white. We are dating or we aren't, offering her space and asked her what I could do to help.
She responded by saying that she needed time to think about it.
During this time I didn't know how to act, couldn't sleep and felt sick of the thought of her with another person. Days later I saw she's been messaging this guy (who I had never heard of) and asked her about him as she was constantly messaging him back and responding to the tiktoks he sent whilst not responding to mine. She got defensive saying he was just a friend.
The next day I confronted her and told her how I was feeling and needed to know that day whether or not we were dating otherwise I'd decide and break up. We talked for 30 minutes and she said we both need to work on our mental health and should break up.
I go home and delete her on social media other than snap (cause we needed to exchange stuff).
It's now been just under a month and I feel I need clarity on the break as I still think about her 24/7 and if she actually loved me or not.
I don't want to get back with her right now (maybe in the future) but I feel as if she never loved me.
Should I ask her about why we broke up or not? if so what should I send?
How can I cope with this break-up?

Thank you,
I was thinking about what you said but just found out she cheated on me and is now dating the new guy. I guess I got my closure.