JSONpath query that returns paths to the matches

I am trying to figure out whether Postgres 14 allows me to find the paths to certain values in the JSON, rather than the values themselves. To illustrate, here is a test query:

SELECT JSONB_PATH_QUERY($${
  "this": "that",
  "that": [{"x": "aaa"},{"y": "missed"}],
  "nested": {
        "deep": {
        "x": "bbb"
      }
  }
}$$, 'strict $.**."x"');

It returns 2 matches: "aaa" and "bbb". However, what I'd like to get instead is 2 paths that point to the matches, i.e.,:

- $.that[0]

- $.nested.deep

Can this be accomplished using means that are available out of the box? If not, what would be a sane way of implementing it?

Thank you for your help,

Alex