You have to tap on the app after you locate it.
Notice here, how the app Midori is shown as OPTIMIZING BATTERY use...
And then when I tap on it...
you can then see that I am given the choice to OPTIMIZE or DON'T OPTIMIZE.
Does the app you are using for the podcast only work for the one podcast, or can it work for many?
If it only does the one, then perhaps you would be better off using a browser for it instead.
I do not know if the app that you are using has settings for cookies, or if there is an automatic timer built in- or if it does if that timer is adjustable.
A browser is much easier to control as far as cookies, and would not have a timer.
But, in my experience, browsers do not tend to play in the background very well.
Yet another thing to consider is whether or not the app that you are using places a constant notification when it is running.
If it does, and you have turned this notification off, this can allow the system to turn the app off more easily.
Because Android systems are becoming more aggressive at turning apps off, some apps are using a 'sticky' notification in order to play continuously.
A browser that I use that does have such a 'sticky' notification as an option is called IDM+.
If this notification is bothersome, typically what you would do is to allow the notification via the app, and then block the notification in your notification settings.