You are probably having trouble because you are using DATETIME_FORMAT() which is turning your date into a text string, which makes it difficult to perform additional math on it. If you remove the DATETIME_FORMAT() from your existing formula, you can use it as the {First of Previous Month} in this formula:
I did longer write-up here in Kuovonne's Guide to Airtable, and included a choice of formulas for both calculating the first of the previous month, and the first Tuesday.
You are probably having trouble because you are using DATETIME_FORMAT() which is turning your date into a text string, which makes it difficult to perform additional math on it. If you remove the DATETIME_FORMAT() from your existing formula, you can use it as the {First of Previous Month} in this formula:
I did longer write-up here in Kuovonne's Guide to Airtable, and included a choice of formulas for both calculating the first of the previous month, and the first Tuesday.