Currently, most podcast listening apps and platforms do not or are not able to provide demographic information (age, gender) about your podcast audience.
However Spotify does provide this information, so here's how to see the demographic information that Spotify provides:
Log into https://podcasters.spotify.com
Click/tap on Catalog, then click/tap on your show
Click on the Audience tab (see first screenshot below)
Change the date range to "All Time"
Scroll down till you see the Age and Gender information
Take a screenshot of each section (see second screenshot below)
You can see demographic information for your show, or on a per-episode basis.
Keep these screenshots handy, as sponsors will most likely ask for this information.
Want to learn more about audience demographics and how to define your podcast audience? Check out: