Only sz should use ß. Ss stays ss even in German-german. Switzerland got rid of the sz/ss distinction a long time ago.
So you need to be culture and word aware to do it „right“.
'sz' for 'ß' is sometimes used to make things roundtrip-proof in capslock, e.g. on military stencils. HTML calls it 'szlig'. Also, some use "Esszet" as the name of the character. But all are wrong in that ß isn't a ligature of s and z, it is a ligature of s and s. The shape of the character stems from the fact that in fractur writing and even some grotesk fonts, 's' at the end of a word was written 's', while 's' within a word was written 'ſ'. Thus the end of a word like Fuss was written Fuſs, giving a ligature of Fuß. No 'z' anywhere.
Originally ß arose as a ligature of s and z, or rather ſ and ʒ. In many older texts, or even current fonts, the second part of the ligature is indisputably a long-tailed ʒ
Only “wrong” in light of current usage, but not historically.
By this measure, the English name of “W” would be wrong because it’s not actually a “double-U” but a “double-V”. But at the time of the letter’s formation, U and V were not yet separate letters.
I always thought that German z used to look something between Ꙁ & з. ʒ looks pretty close so ſз became ß but Latin transliteration rules were ss instead. At least that's what I was taught in German class.