For small problem sizes, you can get a nontrivial improvement by moving the unique up ahead of all the string manipulation:

    jq -r '[path(..)|map(if type=="number" then "[]" end)]|unique[]|join(".")/".[]"|"."+join("[]")'

For larger problem sizes, you might enjoy this approach to avoid generating the array of all paths as an intermediate, instead producing a deduped shadow structure as you go along:

    jq -rn --stream 'reduce (inputs|select(.[1])[0]|map(if type=="number" then "[]" end)) as $_ (.; setpath($_; 1))|path(..)|join(".")/".[]"|"."+join("[]")'

(Note that in either case, you still run yourself into a bit of trouble with fields named "[]", as well as field names with "." in them. I assume this is not a serious issue, since you're only ever looking at this interactively.)