Possible to Group Transaction search by Date Month?

You can use a Date or Character formula to "truncate" dates to the first of the month, produce a year-month format (2021-03 etc.) and just about anything else imaginable. The field type would be Formula (Text) or Formula (Date) depending on what function/output you go with. Play with the formula in non-aggregated result sets so that you get quick feedback. Then, when you have the output you want, group by the formula column.

Also try the Function column for a suitable choice.