Thank you for getting back to me.
I did use your advice, but I couldn't 'refind' the app on the iPhone but it did open and I could see all the podcasts I expected, however when I turned off wifi and 4G I could not open the Podcast App, which told me, regardless of anything else, the app itself was not 'on' my iPhone - I must be being opened 'virtually', or whatever.
So I went to the 2nd step above and looked in the App library with wifi and 4G back on. I was now able to find the app and I decided to delete it from within the App Library, which appeared to work after a few seconds delay.
I then went to the App Store again and this time I did have the option to re-download the Podcast App and it is now working on my iPhone, and in a position I can find with other entertainment apps.
However, being told about the Search feature (which I was unaware of until now) is a very useful function and does rather bypass the need to put apps into specific folders. However, until the 4G or 5G network is improved and my mobile supplier stops charging the earth for data, I will need to download files to my devices.