​Is there a way to see how many providers were engaged by a project manager in a particular month?​

Yes, but I think just outside the system (Excel, MS BI).

How I would approach this: 

Create a view of all the PM's jobs in a particular month (using the date filters), export this data to Excel and do a unique count on the vendor names in Excel. You can also export this for all PM's simultaneously and use the PM column to make a graph in Excel per PM.

I'd be interested to hear other possible approaches.

If you create a pivot table in excel, you can export the whole list (don't need to filter the dates). Dates can be grouped by month.

If there are PM jobs, that provides the necessary information, you could also add a virtual column for let's say a project. Take the date (month) and project manager. Get all the projects jobs (through one of the Services, I think you could start off with the ProjectService), count them and return them. If you do that, you can add it to a custom view in XTRF so you have the data instantly.