Goodness me, does your friend have ANY understanding of abuse at all!? I'd take a good long step back from them for a start.
he was the master manipulator
I would assume his only interest in his child is using her as a means to try to control or otherwise abuse YOU. PPs make an excellent point that he seems mainly to be using the letters to tell you he's watching you. This man is dangerous, OP, I don't mean to frighten you but it is VERY unusual for a parent not even to be granted supervised contact fmsi the courts obviously also think he is dangerous. Lock down all your social media now (or just get rid of it, even better).
Also - he brought up the fact that you're dating in court!? Why? What on earth did he think they would say?? (I assume, "Oh yes, Jack, given that you can't have her any more you're quite right that no one else can either."
Or the good old, "We quite agree with you, Jack, that any attempt to build a life of her own means she's a terrible mother."
)
If he was serious about forging a relationship with his child he would be doing everything he was allowed to do and doing his utmost to demonstrate his consistency. Letterbox contact isn't a peculiar thing in itself, it's quite common in adoptions for example. He could use each letter to tell her what he'd been up to that month and mention things they'd done in the past together that were similar so that she knows he remembers her, for example (even completely uninteresting stuff like, "I had sausages for dinner today. We went to the fair last summer and ate hot dogs from the BBQ cart. I spilled mustard all down myself!"). Though thinking about it I don't suppose he did much with her before? Or he could talk about the weather and ask what she'd been up to - "It's been so wet recently! Have you been puddle jumping? I got all wet going for a run but it was still fun."
Is anyone official screening these letters, OP? I'd be keeping a record of them, using your example:
August 2021: Jack sent a letter that consisted entirely of telling Sarah that he'd seen a parrot. My current profile picture is Sarah and me with a parrot.
July 2021: Jack sent a letter that consisted entirely of telling Sarah that he'd been to Chessigton. My current profile picture is Sarah and me at Chessington.
And so on. Build evidence that he is stalking you (because he is). Contact Paladin for advice.