It’s only complex if your language does not support Unicode properly. In something like rust or python you would just ask for the first character rather than the first byte. And the language will calculate what that is for you.
the second character of sœur (o or the ligature?)
the second character of حبيبي (the canonical form ب or the contextual form ﺒ ?)
the third character of есть (Cyrillic t with or without soft sign, which is always a separate code point and always displayed to the right but changes the sound?)
the first character of 실례합니다 (Korean phoneme or syllabic grapheme?)
the first character of ﷺ or ﷽ ?
The main issue isn't programming language support, it's ambiguity in the concept of "character" and conventions about how languages treat them. Imagine how the letter i would be treated if Unicode were invented by a Turk. The fundamental issue here is that human communication is deeply nuanced in a way that does not lend itself well to systematic encoding or fast/naive algorithms on that encoding. Even in the plain ASCII range it's impossible to know how to render a word like "ANSCHLUSS" in lower case (or how many 'characters' such a word would have) without knowledge of the language, country of origin, and time period in which the word was written.
Just say "I don't have the faintest idea how to do this properly". It would be much less of a problem if people would admit they don't know how and need somebody else's help than it is when they insist it "doesn't really matter" as you have and produce garbage that doesn't work but insist that's just because everybody is holding it wrong.
All of this already standardised in detail in Unicode. There is no ambiguity. Read it some time to mend your ignorance, it answers all your questions with justification, I am willing to spend time on the answers only.
> the second character of sœur (o or the ligature?)
the letter œ, both character (C) and grapheme cluster (GC)
the letter o does not exist in this text (again, according to the standard)
> the second character of حبيبي (the canonical form ب or the contextual form ﺒ ?)
the letter ب, both C and GC
the letter ﺒ is a presentation form and does not exist in this text
> the third character of есть (Cyrillic t with or without soft sign
the letter т, both C and GC
the letter ь, both C and GC, is the 4th in the text
> the first character of 실례합니다 (Korean phoneme or syllabic grapheme?)
the letter 실, both C and GC
the text does not contain the jamo ᄉ
Unicode is not concerned with phonemes, only with writing
> the first character of ﷺ
is entirely itself, the letter ﷺ, both C and GC
> or ﷽ ?
is entirely itself, the symbol ﷽, both C and GC