age: Index is not used in the WHERE clause

Describe the bug

Index is not used in the WHERE clause.

How are you accessing AGE (Command line, driver, etc.)?

• JDBC

What data setup do we need to do?

LOAD 'age';
SET search_path = ag_catalog, "$user", public;

select ag_catalog.create_graph('test_graph');
select ag_catalog.create_vlabel('test_graph','profile');

-- works only for MATCH because GIN only makes sense for pattern matching what MATCH clause is
CREATE INDEX profile_gin_idx ON test_graph."profile" USING GIN (properties);

-- does not work in the where clause
CREATE INDEX profile_pet_btree_idx1 ON test_graph."profile" USING BTREE ((properties -> 'pet'));

-- does not work in the where clause
CREATE INDEX profile_pet_btree_idx2 ON test_graph."profile" USING BTREE (ag_catalog.agtype_access_operator(properties, '"pet"'::ag_catalog.agtype));

------ generate more data -------
DO
$do$
    BEGIN
        FOR i IN 1..10000 LOOP
            EXECUTE format('
                select * from ag_catalog.cypher(''test_graph'',
                $$
                    CREATE (any_vertex: profile { `id`: "%s", `pet`: "%s", `hidden`: %s })
                    RETURN any_vertex
                $$
            ) as (any_vertex ag_catalog.agtype)',
                   (SELECT uuid_in(md5(random()::text || now()::text)::cstring)),
                   (SELECT ('[0:2]={dog,cat,bird}'::text[])[floor(random()*3)]),
                   (SELECT ('[0:1]={true,false}'::text[])[floor(random()*2)])
                );
        END LOOP;
    END
$do$;

What is the command that caused the error?

select
    any_profile
from ag_catalog.cypher('test_graph',$$
    EXPLAIN ANALYZE MATCH (any_profile:`profile` { hidden: false })
    WHERE any_profile.pet = 'dog'
    RETURN any_profile
$$
) as (any_profile ag_catalog.agtype);

QUERY PLAN
Bitmap Heap Scan on profile any_profile (cost=20.08…52.40 rows=1 width=32) (actual time=1.111…22.752 rows=1616 loops=1)
Recheck Cond: (properties @> agtype_build_map(‘hidden’::text, ‘false’::agtype))
Filter: (agtype_access_operator(VARIADIC ARRAY[_agtype_build_vertex(id, _label_name(‘17463’::oid, id), properties), ‘“pet”’::agtype]) = ‘“dog”’::agtype)
Rows Removed by Filter: 3384
Heap Blocks: exact=143
-> Bitmap Index Scan on profile_gin_idx (cost=0.00…20.08 rows=10 width=0) (actual time=1.010…1.010 rows=5000 loops=1)
Index Cond: (properties @> agtype_build_map(‘hidden’::text, ‘false’::agtype))
Planning Time: 0.733 ms
Execution Time: 22.869 ms

Expected behavior Either of two indexes should be used

Environment (please complete the following information):

• Version: [e.g. 1.3.0]

Additional context

As we see from the plan the filter function is applied as:
Filter: (agtype_access_operator(VARIADIC ARRAY[_agtype_build_vertex(id, _label_name('17463'::oid, id), properties), '"pet"'::agtype]) = '"dog"'::agtype)

We also tried to simulate the functional index like this with no luck because there is a mutable function involved: \

CREATE INDEX profile_pet_btree_idx3 ON test_graph."profile" USING BTREE (
ag_catalog.agtype_access_operator(VARIADIC ARRAY[age_properties(_agtype_build_vertex(id, _label_name('16945'::oid, id), properties)), '"pet"'::ag_catalog.agtype])
);

Could it be possible to add an index support for the WHERE clause at least via any functional index by not involving mutable functions ?