How could I perform cohort analysis on Customer data across multiple months

Question

As the question says, I'm looking to conduct cohort analysis on customers to understand retention rate and effectively create a filter on Looker Studio to scope it to just a cohort of customers.

I've got the following code that scopes a field to customers who made their first transaction in Sep 2023

  WHEN EXTRACT(YEAR FROM TransactionDateFixed) = 2023 
       AND EXTRACT(MONTH FROM TransactionDateFixed) = 9 
       AND FirstTransaction = 'TRUE' 
  THEN 'Sep23 Cohort'
  ELSE 'Other'
END

But the problem is when I add a filter to any visuals and set Include for the Field which is named Sep 23 FTD Cohort and Contains "Sep" it limits the data to just the month of September 2023.

I was hoping it would scope it to any date range but only limit it to customers who made their first transaction in Sep 2023.

Is there a nicer way to do this in Looker Studio? I have other columns such as ExternalCustomerId which is a way to identify customers across multiple months if that helps.