When we use still not, there is a sense of looking back to the past. But not yet has the sense of looking toward the future.
She still hasn’t got a job. (looking back: she hasn’t had a job since January and the situation is continuing.)
She hasn’t got a job yet. (looking forward: she hasn’t got a job now, but we’re hoping she’ll get one soon.)
I still can’t speak French, after staying here for two years.
I can’t speak much French yet, but I hope to learn soon.