Non-BMP code points (those between 0x10000 and 0x10FFFF) must also be handled correctly: answers should produce actual character counts in code points, not in code unit counts.
Therefore a string like "𝔘𝔫𝔦𝔠𝔬𝔡𝔢" (consisting of the 7 Unicode characters U+1D518 U+1D52B U+1D526 U+1D520 U+1D52C U+1D521 U+1D522) is 7 characters long, '''not''' 14 UTF-16 code units; and it is 28 bytes long whether encoded in UTF-8 or in UTF-16.
For example, the string "J̲o̲s̲é̲" ("J\x{332}o\x{332}s\x{332}e\x{301}\x{332}") has 4 user-visible graphemes, 9 characters (code points), and 14 bytes when encoded in UTF-8.