"1. What could he possibly want to blackmail OP about?"
I will attempt to explain, but you're not going to like it.
I once dared to take interest in something myself and XP were passing on holiday. He immediately started getting angry and physically dragged me away by the waist and arm. I was confused and upset at the time but didn't think anything of it, even though I knew in my mind that this wasn't a one-off incident.
Months later I realise that it was because the woman in his "script" (as I think dignified explained) would not have wanted to see it until another day, and would've been obedient enough to accept this.
Not following the "script" is why the taking of photographs of me naked without my permission started that night.
It's not about what the person wants (and this is why people find this kind of blackmail situation so difficult to believe, as you yourself understandably seem not to) - it's that he gets what he wants.
"2. Who gives a toss if OP sent messages anyway - hardly blackmail material"
It's easy to control someone or to turn others against them if you can make out they are "dirty".
It was this kind of behaviour, of course, which was why I initially did not tell anyone when he raped me.
Now, before anyone says "oh you're projecting" and "your imagination is running away with you" etc., I'm not saying OP's DP is a rapist! but at the same time I wouldn't count out the possibility of a darker intention than just a sexual fantasy.
"3. The texts would need to come from a number registered in the OP's name anyway - which I doubt."
Who do you think will get to the point of asking? and even if they did, if they are prepared to blackmail with false messages, what do you think they are prepared to say or do when someone wants proof that it is OP's number?