Adding the proper window specification for the "OVER" clause plus DISTINCT helps to achieve some resemblance of STRING_AGG for the simple  ascending order:

select distinct
    object
    ,array_join(array_sort(collect_set(property) over (partition by object order by property ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)), ',') as properties
from 
    (
    values
    ('object 1','C')
    ,('object 2','F')
    ,('object 1','B')
    ,('object 2','E')
    ,('object 1','A')
    ,('object 2','D')
    ) as t(object,property)
order by object