Our 6.5 yo has never slept well, stopped napping before she was 2, and has an incredibly hard time some nights calming down enough to sleep. She also freaks out about being unable to sleep or other issues (hyperventilating, sobbing, etc). She's also neurodivergent which likely has an impact the sleep issue and her response, so carry on with reading skeptically.
We have tried just about all of the recommendations in this thread with varying levels of success. Some nights there's nothing that helps. So, we just stick it out with her until she's calm enough to fall asleep.
If she's worried about something, we will let her talk as much or as little about it without dismissing it or telling her it's not a big deal. She has lots of what ifs, and I've found that the only way to get through it is to respond "I'm not sure, what do you think would happen if XYZ happened?" Letting her voice it takes the edge off.
Sometimes she's too worried about it. I'll give her the open space to talk, and if she doesn't take it, after a very long time I'll say something like "there's something you're really worried about and you're too worried to talk about it. If you want to talk about it or not, I still love you." It usually comes out after lots of silence, or she's able to sleep.
Finally, if she's freaking out about specifically being unable to sleep which has strangely actually been happening this week, we have found that addressing the frustration side of not being good at falling asleep is the key here, not the worry. Letting her know that it's frustrating to learn new things like sleep, especially when she's really good at some things, and that it doesn't mean that anything is wrong with her. That approach has worked much better than some of the anxiety techniques.
One of my favorite parenting books of what feels like hundreds over the last 5 years is Good Inside. Her approach resonates well with my personal philosophy, DW approves and uses techniques from it, and most importantly DD responds well to the approach.