Is double chin Botox effective even if there is a lot of fat in the chin area?

Lately, I've been under a lot of stress because the fat under my chin folds thickly whenever I take a picture or lower my head. It has been upsetting more than once, especially when I look in the mirror. Even though I clearly hold my head up, I still get a double chin.

Although the principle of Botox is to reduce muscle, I believe that in this case, some fat should also be reduced. However, given that this is a double chin caused by fat accumulation in the jaw area, would Botox alone be effective for the jaw fat?

Alternatively, please let me know if there are any other procedures available, such as fat-dissolving injections.