My thoughts are that there does come a time when you need to allow teenagers their privacy online. And 13 is a reasonable age to start that, so your thoughts of allowing and respecting her privacy are reasonable snd OK. Thst said, it's a gradual change towards that privacy since to earn thar privacy she needs to show that she takes the responsibility for the risks seriously.
Until she takes responsibility for those online risks herself, the responsibility is yours as parent. So therefore you need to check up on her, to keep her safe online, and there's no shame or decipt in that.
Just explain that too her - the more you check and see she is able to manage the responsibility to stay safe herself, the less you will need to check. But currently you need to check more - not to catch her out or get her into trouble - but because it's your job as parent to make sure she is safe.
Given shes instigated and willingly participated in this sexting its really important you don't make her feel ashamed for doing it. Feeling aroused, masterbating and wanting to feel sexually desired is normal and age appropriate at 13.
Worry if the conversations are one-sided, have elements of control or cohesion, if there's a power imbalance or if the language used is highly inappropriate rather than just sexual. But if its basic sex talk, oral sex talk, mutual maturation talk etc, as distasteful as that might be for you to read (and her to know you've read) it isn't age inappropriate.
If it is "just" sex talk, instead of focusing on the content you could focus on the fact that it's written digitally. That means it could be screen shot and used against her. Children are at risk of being blackmailed, for example. Or she could fall out with this boy then he could send the screen shot to her school friends, her teachers, her family. Screen shot conversations can also be photoshopped and changed.
You might also need to think about - why is she seeking this attention online? Low self esteem? Mental health support might be needed. Lonely and wants more friends? Talking to school or extra curricular activities might help. Does she feel unattractive and so valued the ego boost? Shallow as it sounds, but helping her focus on looking good with clothes, skin care, hair tutorials might help. Could be any number of things.