Are links in Podcasts show notes supposed to be "live"?
Apple's podcast specs explicitly discuss how to embed HTML links within the Summary field: 


  Text Encoding
  
  Use plain text UTF-8 encoding for your podcast feed (no markup or HTML, except as described below).
  
  Tag values are limited to 255 characters, except for , which can be up to 4000 characters. Don’t add leading or trailing spaces to your values.
  
  Enclose all portions of your XML that contain embedded links in a CDATA section to prevent formatting issues, and to ensure proper link functionality in the Podcasts app. For example:
  
  &lt;itunes:summary&gt;&lt;![CDATA[&lt;a href=“https://www.apple.com”&gt;Apple&lt;/a&gt;]]&gt;&lt;/itunes:summary&gt;
  


Several popular podcast clients support this —  Overcast, Pocket Casts, Downcast, among others — ,and I believe Podcasts on iOS does now as well. 

See for example this screenshot from Macstories' review of Overcast:

[