I suspect that $1{$2} is recognized as addressing an associative array, but I could not find any mention in the documentation about such an expansion in the substitution part of a RE.

See Quote and Quote like Operators:

... In the following table, a {} represents any pair of delimiters you choose.

Customary   Generic         Meaning     Interpolates
              ...
             s{}{}       Substitution      yes*
              ...
* unless the delimiter is ''.
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Where "interpolates" means the same thing as what happens to strings in double quotes, like "$hash{$key}", or, in your case, "$1{$2}". The error message gives you a hint: "Use of uninitialized value within %1 in substitution iterator" - so yes, $1{$2} means the same as $x{$y}, that is, access the hash %1 and fetch the key named by the string stored in $2. Your solution of adding the backslash is fine.