Here’s what I found.
Count
143,859.¹
Full table: https://unicode-table.com/en/#basic-latin
Methodology
This short article assumes that by now, every useful/usable/commonly-used character has been encoded and added to the unicode standard.
This is not necessarily the case. In fact, “Unicode standard doesn’t freeze, it continues to evolve.”²
Definitions
Character (computing): In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language.³
Unicode is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world’s writing systems.