The Sütterlin alphabeth was introduced by the graphic designer Sütterlin in the 1920s and was the handwriting in German schools 1935-1941. It was a slightly simplified version of Kurrent. Before that time the usual handwriting style in Germany (since the 1500s) in german language was Kurrent (also known as Kurrentschrift, Alte Deutsche Schrift ("old German script") and German cursive) which was used also in Switzerland till 1900s and in Austria till 1941 (and still taught in schools after 1945; I learned it besides the Ausgangsschrift in elementary school 1955-1959).
The letter $\wp$ is, originally (in my eyes, and as I learned in lecture classes), just a capital P in Kurrent, written in a slightly elaborate way. I would say that the Weierstrass-P symbol $\wp$ was introduced by Donald Knuth as a special math TeX-symbol, :) . I would have used $\mathfrak P$ before learning about $\wp$ in the question.
See here for six letters by Gauss written in Kurrent.