That already is ambiguous without considering text encodings or even computers.
Sort order depends on locale (example, “in Lithuanian, "y" is sorted between "i" and "k"”) and within some locales even on the goal of the sorting (example: “in German dictionaries, "öf" would come before "of". In phone books the situation is the exact opposite.”
(Both examples taken from https://unicode-org.github.io/icu/userguide/collation/, which has many more examples)
Also, on that “one code point in unicode does not necessarily map to one character on the screen”, I think it’s important to use consistent terminology. The screen doesn’t show characters but glyphs.