MySQL 8.0

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create table t (
    id int not null primary key,
    customer_id int,
    start_at date,
    end_at date
)
insert into t (id, customer_id, start_at, end_at) values
(44,    37, '2019-03-21', '2019-03-21'),
(17819, 37, '2020-03-23', '2020-03-23'),
(22302, 37, '2020-04-24', '2021-07-25'),
(42213, 37, '2021-04-25', '2023-04-26'),
(92013, 37, '2023-04-26', '2024-04-26')

Records: 5  Duplicates: 0  Warnings: 0


set @date1 = '2020-01-01';
set @date2 = '2020-12-31';

with cte1 as (
    select customer_id, start_at, end_at
    from t
    where start_at <= @date2 and end_at >= @date1
), cte2 as (
    select *, case when start_at <= max(end_at) over (partition by customer_id order by start_at rows between unbounded preceding and 1 preceding) then 0 else 1 end as newgrp
    from cte1
), cte3 as (
    select *, sum(newgrp) over (partition by customer_id order by start_at) as grpnum
    from cte2
), cte4 as (
    select
        customer_id,
        datediff(
            least(max(end_at), @date2),
            greatest(min(start_at), @date1)
        ) + 1 as diff
    from cte3
    group by customer_id, grpnum
)
select customer_id, sum(diff) as total
from cte4
group by customer_id


customer_id
total


37
253