User profile fields: Get count of fields with value XYZ
You can create a view as a block using users as the base table (Structure>Views>Add View and set show=Users and check "Create a Block").  Then turn aggregation on in the advanced settings. Then add the field_category field and select "Group Field". Next add field_category a second time and select "Count". This should give you a column of each category, and the count of how many users exist in each category.

Finally, add the block to the frontpage in the Block Layout.