FWIW, I advocate ~ as array append (a la perl6/raku strings) (and also as wedge product on vectors, * being dot product). It works well with x^y as exponent/repeat, since the rhs is qualitatively different anyway[0], and also gives you (with +) a sum-of-products/dioid/semiring structure for concatenation and alternation on regular expressions. Admittedly, you still don't have a sensible semantics for division, but that's true of plenty of other product operators (even int is iffy - either not closed (div-as-float/rational/etc) or not a multiplicative inverse (divmod)).

0: In particular, exponentiation by natural numbers (or positive integers for things like nonempty lists that deliberately exclude the multiplicative identity) is almost always well defined[1], even if the thing you're exponentiating bears no resemblance to a natural number.

1: Although note than with vectors and dimensional quantities (eg meters), x^2/x^3/etc are all different types: area/volume, bivector, etc.