The ß is kind of funky "s"

It is actually a ligature of s and z, or at least, it started as one. That also gave it its name, Eszett: s-z. It is way more obvious in Fraktur, where you have two different forms of the lower case s. The "short" s that looks familiar and is generally used at the end of syllables, and the long s that is generally used at the beginning or in the middle of a syllable. It looks more or less like an f without the horizontal line. For the sharp s (which is also an alternative name for the Eszett), the s was doubled, depending on time and font, either as two long s or two short s or a long and a short s. The combination of long s and short s was alternatively printed as long s and z, which were merged in a ligature. In the following years, ß and ss became slightly different, annoying generations of students. The 1996 orthography reform attempted to get rid of ß in many places.

and there is no uppercase version of this single lowercase letter.

There are reasons: The upper case s was always S, for both long s and short s. The sharp s, written as ss (two longs, two shorts, or one long and one short) would always be written in upper case as SS. No extra rules or letters needed. The alternative form sz, printed as ligature of long s and z, would be written in upper case as SZ. Again, no extra rules or letters needed. But then, people started to treat the s-z ligature as a new and unique letter and forgot that it was a ligature. That caused the "strange" rule of "converting" ß to SS when converting to upper case, except where misunderstandings may happen, in that case, ß should be "converted" to what it represents, SZ. That rule is rarely used, most times, context is sufficient. Maße (measurements) and Masse (mass) are a classic example, both can be written as MASSE, but if misunderstandings may happen, Maße must be written as MASZE.

At this point, rules for converting to upper case become really hard for computers. And so, ß was finally treated as a regular letter instead of a ligature and got its own dedicated upper case form (see Re^3: Memory Leak with XS but not pure C). The allocation in Unicode is a little but far away from ß and the other glyphs used in German, keyboard support sucks (Shift-ß gives ?, not the upper case ß), but at least, there is an upper case ß, now that the new orthography tried to eliminate it.

Alexander