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I would love some advice for what symbol to use and best implement it?

<< Notation`;
Notation[ParsedBoxWrapper[
RowBox[{"x_", " ", "jn", " ", "y_", " "}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[
RowBox[{" ", RowBox[{"Join", "[", RowBox[{"x_", ",", "y_"}], "]"}]}]]]
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~Join~ can already serve as an infix operator. If you want something more concise I recommend choosing one of the existing operators without a built-in meaning. Simply:

UnionPlus = Join;

{1, 2}⊎{3, 4, 5}
{1, 2, 3, 4, 5}

(Use InputAliases for fast entry.)

If there are none there that you like you might use Rojo's method from Is it possible to define custom compound assignment operators like ⊕= similar to built-ins +=, *= etc?

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