It's the Carret Notation: https://en.wikipedia.org/wiki/Caret_notation

That's because C-J IS ANSI Carriage Return. It's basically the absence of any special treatment.

You meant ASCII Line Feed, ne?

Yes, shame on me. Should have conducted ascii(7) before making bold statements.

       Oct   Dec   Hex   Char                        Oct   Dec   Hex   Char
       ────────────────────────────────────────────────────────────────────────
       000   0     00    NUL '\0' (null character)   100   64    40    @
       001   1     01    SOH (start of heading)      101   65    41    A
       002   2     02    STX (start of text)         102   66    42    B
       003   3     03    ETX (end of text)           103   67    43    C
       004   4     04    EOT (end of transmission)   104   68    44    D
       005   5     05    ENQ (enquiry)               105   69    45    E
       006   6     06    ACK (acknowledge)           106   70    46    F
       007   7     07    BEL '\a' (bell)             107   71    47    G
       010   8     08    BS  '\b' (backspace)        110   72    48    H
       011   9     09    HT  '\t' (horizontal tab)   111   73    49    I
       012   10    0A    LF  '\n' (new line)         112   74    4A    J
       013   11    0B    VT  '\v' (vertical tab)     113   75    4B    K
       014   12    0C    FF  '\f' (form feed)        114   76    4C    L
       015   13    0D    CR  '\r' (carriage ret)     115   77    4D    M

In fact, without some fairly new (and poorly supported) extensions, it's impossible for an application running in a terminal to distinguish between ^J and a "real" press of the return key. The same goes for tab vs. ^I, Esc vs. ^[, and so on.

Claude Code does distinguish between the two. Pressing the Enter key submits the query, pressing ^J inserts a newline.

That's maybe, because (I was wrong and) it's LF, but pressing return produces CR, which is differentiable by an application.