It's a cursive script which at the bare minimum can work as an abjad, but is usually an abugida with the vowel signs (especially when the diacritics are used).

And yep, it's mainly inspired by Han-geul and the sound inventory is largely taken from Jawi, the Malayo-Arabic script. With one more extra consonant coming from historical Cantonese. The idea of a cursive script also comes from the Jawi script as well, but written left-to-right instead.

Elements from Han-geul alone couldn't make enough new letters for the new sounds, so I'll have to borrow inspirations from elsewhere. Sometimes while adapting Han-geul letters into cursive form (especially ㅂ!!!), I run into trouble and this is also where other inspirations come in handy. Speaking of which, I have another post coming soon which will break down the origins and inspirations of a few example letters.

I use it for handwriting from time to time, especially when feeling either secretive or bored. Sadly I haven't yet digitalized the script into a proper font, so I couldn't use it as much as I wish.

Oh yeah, I've finally posted the breakdown for some letters here

Btw for the mysterious script that eluded you, were you referring to the Phoenician script?