Another possible answer, if you are willing to update the schema, would be to store the previous value in another column:

ALTER table my_table add column prev_hash text;

INSERT INTO my_table (
    id, -- unique key
    hash
) VALUES (
    1,
    'a'
) ON CONFLICT (
    id
) DO UPDATE SET
    hash = excluded.hash,
    prev_hash = my_table.hash
RETURNING
    id,
    hash,      -- will be the new hash
    prev_hash  -- will be the old hash

I did end up finding a workaround, though it doesn't strictly guarantee atomicity, but in general could be a good strategy depending on your use case.

INSERT INTO my_table (
    id, -- unique key
    name,
    hash
) VALUES (
    '4b544dea-b355-463c-8fba-40c36ac7cb0c',
    'example',
    '0x0123456789'
) ON CONFLICT (
    id
) DO UPDATE SET
    name = 'example',
    hash = '0x0123456789'
RETURNING
    name,
    hash, -- will be the new hash
    (SELECT hash FROM my_table WHERE my_table.id = '4b544dea-b355-463c-8fba-40c36ac7cb0c') -- will be the old hash
    ;

You can use CTEs.

If you need exact one column and one row, below is simpler approach.

with prev as (
    select name
    from student
    where id=$1
)
insert into student(id, name)
values($1, $2)
on conflict (id) do update
    set name=excluded.name
returning (select name from prev);

For your need, can use 2 CTEs:

with prev as (
    select *
    from student
    where id=$1
), upd as (
  insert into student(id, name)
    values($1, $2)
    on conflict (id) do update
        set name=excluded.name
)
select * from prev;

Examples

-- Bootstrap script to create tables and insert some data
create table student (
  id serial primary key,
  name text
);

insert into student(name)
values ('st1'), ('st2');

-- returns 'st1'
with prev as (
    select name
    from student
    where id=1
)
insert into student(id, name)
values(1, 'st1-altered')
on conflict (id) do update
    set name=excluded.name
returning (select name from prev);

-- returns id: 2, name: 'st2'
with prev as (
    select *
    from student
    where id=2
), upd as (
  insert into student(id, name)
    values(2, 'st2-changed')
    on conflict (id) do update
        set name=excluded.name
)
select * from prev;

-- returns nil (since there's no previous value)
with prev as (
    select *
    from student
    where id=3
), upd as (
  insert into student(id, name)
    values(3, 'st3')
    on conflict (id) do update
        set name=excluded.name
)
select * from prev;