Postgres like_regex with variables

I want to query a JSONB array using a regex filter. Following the docs , I should be able to do:

WHERE jsonb_path_exists(
  data, '$.value[*] ? (@ like_regex $foo flag "i")',
  jsonb_build_object('foo', 'demo')
)

but I'm getting an error:

ERROR: syntax error at or near "$foo" of jsonpath input

I think it's because $ is a valid regex character? Here is some demo data:

INSERT INTO table_data (fields) VALUES
	 ('[{"value": "Sales"}]'),
	 ('[{"value": "CEO Staff"}]'),
	 ('[{"value": "Procurement"}]'),
	 ('[{"value": "CEO Staff"}]');

I wish to query all that have a value containing 'ceo'.