Use a filter to identify all months with dates inbetween a date range

I have a date range column and alongside this I have created copy columns splitting it to have a start date column and and end date column.

I want to select a month from the calendar as a filter so that my data shows data lines within a range than includes the month i would have selected - even when that month is not the start month or the end month.

For example:

Line 1 - start date: 12/01/2023 with end date: 03/03/2023

Line 2 - start date: 14/04/2023 with end date 23/07/2023

Using a month filter - I want to be able to select e.g. 'June 2023', then line 2 above should show as the result since the range is from April to July 2023, or if i select February 2023 then line 1 should show in the result since the range is January 2023 to March 2023.

thanks for your help in advance