That letter, the capital eszett, has existed in German typefaces since at least 1905:
> Historical typefaces offering a capitalized eszett mostly date to the time between 1905 and 1930. The first known typefaces to include capital eszett were produced by the Schelter & Giesecke foundry in Leipzig, in 1905/06. Schelter & Giesecke at the time widely advocated the use of this type, but its use remained very limited.
Eszett is usually just a lower-case form; it is most often upper-cased to SS, or two capital letter esses, being an example of how changing case does not always preserve the number of letters in a text. Capital eszett is very rare, but it was in uncommon usage in German text, and so it was added to Unicode.
The newly added letter is the "capital letter Eszett", which did not exist until recently. One could argue that this new letter is not really needed, as Eszett does not appear in capitalized form except when a word is in all-caps, and was then simply written as "SS".
SZ hasn't officially been an option at least since 1996.
ß is both visually and from its name (‘s’ ‘z’) a ligature of s and z (“Eszett” in English is “ess-zed). An ss ligature would look like a double integral sign. “Sz” seems like a better way to represent that sound, so I don’t know why it morphed into “ss”
Greek has two characters for s, one for use in the middle and one for the ends of words. English lost this in the late 18th or early 19th century (look in the Declaration of Independence for examples). German kept it longer, at least in Fraktur, which included other standard ligatures, even in handwritten text, such as ch, tz et al. The Umlaut mark can also be considered a ligature for E which is how it was originally drawn.