SSIS – Extract SQL Data and Split Across Flat Files Based on Row Count

I have created a simple SSIS package that queries a table and extracts data to a flat CSV file. In production this extract could be millions of rows and I want to split the flat file destinations into multiple files based on row count.

So create new file each time we hit 100000 rows with filenames something like

• SomeName_01_date.csv
• SomeName_02_date.csv

I have found a paid for tool by ZappySys that will do this but cannot work out how to do it with just the normal SSIS toolbox, I may be missing something really simple.
I have found other posts and videos but some of them involve using additional code outside of the normal tool set, such as the techbrothersit website.

Edit:
After reading up and from the comments this looks to be harder than expected.
If I change process to split the flat files based on a date column in the table would that be more straight forward?

Table has a short date column in this format 2020-07-30, each CSV file would contain just one days worth of extracted data (could be 100K+), that data is then deleted from the table. The deletion will occur after all data has been extracted.

I am trying to use a foreach/forloop container but struggling as this is totally new to me, any help would be appreciated.