If you have your podcasts set to stream, instead of download, the file size is listed above each episode in feed right next to the upload date. Just set podcasts to stream in settings.
Some RSS feeds have a glitch causing size/length to not show until you play it, but it’s very rare & usually only happens on certain RSS feeds converted from a website. That bug, in my experience, isn’t on AntennaPod’s end and often resolves on its own.
There’s no way to gauge how much cell/WiFi data a download or stream will use beforehand. Knowing the file size is more than enough, and doesn’t matter if you’re streaming. Just clear app cache regularly if tight on storage space.
EDIT: Check your feed update interval settings. The less often it refreshes feeds for new episodes, the less background data & battery will be used. Set it to largest interval & only update on WiFi.
Just to clarify, the file size does appear in multiple places except in the episode details page, where only date & episode length are displayed.
In my mind, the episode details page is the one place where everything about an episode should be displayed with nothing held back.
(In fact, one thing I wish was also displayed here was a hyperlink to the individual episode media file, rather than hiding it behind the 3-dot → Share menu. Also nice to have would be the chapter details too, if they exist. What else…? )