It seems like "ASCII QR" is a play on "ASCII art", which is an existing compound word with a specific history and meaning that the term "text art" simply does not have. When I think of ASCII art, it reminds me of old plain-text video game FAQs, which often included elaborate ASCII art throughout. "Text QR" or "Unicode QR" does not have that association.
Of course; but ASCII art only uses ASCII characters. Back in the BBS days you could use ANSI to give you different characters and colors; but that was called ANSI, not ASCII.
"Unicode QR" is probably the best term for what's happening here.
It's typically used to refer to certain Microsoft 8-bit code pages, like Windows-1252, that extend 7-bit ASCII to 8 bits. My understanding is that these code pages were proposed as an ANSI standard, but never adopted. ISO 8859-1 (Latin-1) is similar but not identical to Windows-1252 (Latin-1 has control characters in some positions where Windows-1252 has printable characters -- and Unicode inherits those control characters from Latin-1.)