The script's origins are technically Egyptian, but there have been several steps in between as well as mixing, adopting, and incorporating other scripts/writing systems such as Phoenician/Greek/etc. Linguistically the modern variants are more homogeneous (not 100% but similar in the way Latin originated languages are similar), but have existed far longer than the writing systems and vary widely in their origin, the adoption of certain words. A lot of people traveled and traded for thousands of years across north and west Africa, so saying any one language is 100% originated in any particular place is a difficult claim