Any other easy method available to fix this issue with search_path?
The direct solution here is to rewrite the expression, avoiding "IS DISTINCT FROM":
not("new"."path" operator("util".=) "old"."path") and (coalesce("new"."path", "old"."path") is not null)
This is needed because you need to schema-qualify the location of the = operator which requires using the "operator(...)" syntax.
That said, it might be easier, if less performant, to remove the WHEN condition and place an equivalent expression within the trigger function itself. If the function is defined with a "SET search_path" clause that should ensure that the function body is evaluated with the "util" schema in the search_path and thus the "util".= operator will be found.
