Ah, well now I feel silly. I didn't notice the triple dot menu button at the end of the "Episodes" entries. However, it does look like you can only do this from a podcast you've already started playing from elsewhere, bringing up the "Podcasts" section and clicking the menu buttons on each podcast only lets me view the podcast's home page, or its RSS feed directly (instead of letting me see a list of episodes and choosing one from said list).

So it seems like you could do Mobile (start episode) -> Web (resume episode, then pause again) -> Mobile (finish episode) but you can't do Web (start episode) -> ...

However I could be of course overlooking something again 😅