Hm, both the main article and your link are wasteful for strings of length 13-15, which are still pretty common. As a rule for SSO, if you're already take up the bytes unconditionally, it's going to be worth complexifying your "size" calculation to squeeze a little more into the no-alloc case.
That said, note that there are a lot of strings around 20 bytes (stringified 64-bit integers or floats), so pushing to 24-1 is a reasonable choice too.
I'd use 3 size classes:
* 0-15 bytes, stored in-line. If you need C-string compatibility (which is fairly likely somewhere in your application), ensure that size 15 is encoded as a zero at the last byte.
* up to 3.75GB (if my mental math is right), stored with a mangled 32-bit size. Alternatively you could use a simpler cutoff if it makes the mangling easier. Another possibility would be to have a 16-bit size class.
* add support for very large strings (likely with a completely different allocation method) too; a 4GB limit sucks and is easily exceeded. If need be this can use an extra indirection.
Honestly, with a 16-byte budget, I'd consider spending more of that on the prefix - you can get 8 bytes with enough contortion elsewhere.
Duplicating the prefix is probably worth it in more cases than you might think, since it does speed up comparisons. Just remember, you have to check the size to distinguish "a\0" from "a" too, not just from "a\0\0\0\0".