query customer retention over range

Question

I am trying to find the best way to accomplish the following.

• Get the beginning customer count, which carries from the previous day
• Get New Customer count
• Get the number of Customers who have not come in since the prior month
• Get the number of Customers who have come back after lapsing
• Get the number of total customers

The following example

Customer ID	Store ID	Date	Amount
1	1	1/2/22	1.00
2	2	1/2/22	2.00
1	1	2/2/22	1.00
3	2	3/2/22	1.00
2	2	3/2/22	1.00
1	1	3/2/22	1.00
1	1	4/2/22	1.00
4	1	4/2/22	1.00
2	2	4/2/22	1.00

The result would be

Date	Store	Beginning	New	Dropped	Returned	Total
1/2/22	1	0	1	0	0	1
1/2/22	2	0	1	0	0	1
2/2/22	1	1	0	0	0	1
2/2/22	2	1	0	1	0	0
3/2/22	1	1	0	0	0	1
3/2/22	2	0	1	0	1	2
4/2/22	1	1	1	0	0	2
4/2/22	2	2	0	1	0	1

I kind of have a query, but it's not getting the right results

WITH customerset AS (
    SELECT
        location_id,
        date,
        array_agg(DISTINCT customer_id 
                  ORDER BY customer_id ASC) 
                  AS customer_ids
    FROM customer_orders
    GROUP BY
        location_id,
        date
)
SELECT
    cset.location_id,
    cset.date,
    array_length(cset2.customer_ids, 1) AS beginning,
    array_length((past2.customer_ids - cset.customer_ids), 1) AS dropped,
    array_length((cset.customer_ids - past2.customer_ids), 1) AS returned
FROM
    (
    SELECT
        ords.location_id,
        ords.date,
        array_agg(DISTINCT ords.customer_id 
                  ORDER BY ords.customer_id ASC) 
                  AS customers_id
    FROM customer_orders ords
    GROUP BY
        ords.location_id,
        ords.date
    ) cset
JOIN
    customerset cset2 
     ON cset.date - '1 month'::interval = cset2.date
    AND cset2.location_id = cset.location_id
GROUP BY
    cset.location_id,
    cset.date,
    cset2.customer_ids,
    cset.customer_ids
ORDER BY
    cset.date ASC