Count of available items with start and end dates grouped by month

I am working with PSQL/pgAdmin, looking to get a total # of inventory grouped by month for the year. I've tried a generated_series, but when I try to use a Count Filter it seems to ignore the date.

My attempt

select
g.day::date,
count(item) filter(
  where install_date <= g.day+'1month'::interval
  and (removed_date is null or removed_date < g.day+'1month'::interval))
FROM table
CROSS  JOIN generate_series('2024-01-01'::timestamp, '2025-01-01'::timestamp, '1 month'::interval) AS g(day)
group by 1,2

As an example:

So the results would look something like

All months are generated within a date range.

Each month is then compared with install_date and removed_date should be greater than the month_start so that it is excluded from that month.

Fiddle

WITH month_series AS (
    SELECT generate_series('2024-01-01'::date, '2024-12-01'::date, '1 month'::interval) AS month_start
)
SELECT 
    to_char(month_series.month_start, 'Mon YYYY') AS month, 
    COUNT(i.item) AS install_count
FROM 
    month_series
LEFT JOIN 
    inventory i 
    ON i.install_date <= month_series.month_start 
    AND (i.removed_date IS NULL OR i.removed_date > month_series.month_start)
GROUP BY 
    month_series.month_start
ORDER BY 
    month_series.month_start;

Output