ASCII doesn’t go above 127, and your link is to Windows-1252, which is obsolete.
In modern computer systems, the character is U+2019 RIGHT SINGLE QUOTATION MARK in Unicode. I think Chapter 6 – Unicode 17.0.0 is the right reference for its usage as an apostrophe:
U+0027 ’ APOSTROPHE is the most commonly used character for apostrophe. For historical reasons, U+0027 is a particularly overloaded character. In ASCII, it is used to represent a punctuation mark (such as right single quotation mark, left single quotation mark, apostrophe punctuation, vertical line, or prime) or a modifier letter (such as apostrophe modifier or acute accent). Punctuation marks generally break words; modifier letters generally are considered part of a word.
When text is set, U+2019 ’ RIGHT SINGLE QUOTATION MARK is preferred as apostrophe, …
I’d honestly recommend looking at the Unicode standard itself whenever trying to understand what a specific Unicode code point (character-ish) actually means.