I think something that adds to the TP in diamond form confusion is that some writers try to depict a scene in which she's engaging in TP activity just as she left diamond form... and the artist, for visual effect, has the TP speech bubble appear while she's mid-transformation. If the artist can't make the mid-transformation part clear, it may be confusing. I remember a specific Phoenix Endsong panel where this happens.
Emma was confirmed a latent TK user in Generation X. Synch was able to use telekinesis when synching with her (and the narrator specifies it is Emma's powers he's using, not M's), and there's an issue where she unconsciously has objects levitating while she's asleep.
But that was before she moved to the big leagues, writers and editors during that time didn't have to worry about her powers being the same as Jean's and Psylocke's since she wasn't going to be around them. Once Morrison came in, TK potential was dropped in favor of the diamon form, and for all intents and purposes her TK doesn't exist anymore. Specially because now it would be even worse, with Charles developing TK as well and with Rachel and Kwannon having that same powerset.
But it is as you say, the official explanation is that it is a secondary mutation, and not related at all with TK. The headcanon that her latent TK has something to do with her diamond form is interesting, but I think that's not something that will ever be addressed on panel. It could work like Avatar's earthbenders being able to bend eiter metal or magma, but not both, because to bend metal one has to be strict and stern in personality, while to bend magma one has to be malleable. Maybe during the Genosha attack all of Emma's TK potential turned to her own preservation and "crystalized" as a diamond and remained as such.
Emma's diamond form is only named "diamond" due to appearance, but in-universe it's been shown to be far stronger than real-world diamonds. Diamonds in real life are very hard but also very brittle... while her DF isn't brittle and she has survived the Genoshan attack, a celestial blast, adamantium claws, etc. thanks to it. If she was like our diamonds, she would have shattered many times more already haha.