With minor modifications it worked, thanks!
Had to add group_by and coalesce to deal with nil count values.
Here is the final working query:

   orders_query =
      from(o in Order,
        left_join: s in assoc(o, :shipments),
        where: not o.archived and is_nil(s.id),
        group_by: o.company_id,
        select: %{company_id: o.company_id, count: count()}
      )

    shipments_query =
      from(s in Shipment,
        inner_join: o in assoc(s, :order),
        where: is_nil(s.batch_id),
        group_by: o.company_id,
        select: %{company_id: o.company_id, count: count()}
      )

    Company
    |> filter_by_user(user)
    |> only_active(true)
    |> join(:left, [c], o in subquery(orders_query), on: o.company_id == c.id)
    |> join(:left, [c], s in subquery(shipments_query), on: s.company_id == c.id)
    |> group_by([c, o, s], [c.id, o.count, s.count])
    |> select_merge([c, o, s], %{
      orders_count: coalesce(o.count, 0),
      shipments_count: coalesce(s.count, 0)
    })
    |> Repo.all(prefix: tenant)