Ok, so after watching faaaaar too much of this cr@ppy TV show, I managed to collect some more data/files.
We all knew this would be the case, but for completeness, here we go… I started to record a TV show that was being aired as Interlaced; watching it through Chrome, I could see it was not deinterlacing (I took a screen grab); I waited for the adverts/commercials, and then used wget to dump out a short clip direct from HDHomeRun; as expected the small section I captured is in Progressive… At this point I stopped the recoding of the show and checked back in PMS and sure enough Plex has identified the show as Interlaced.
For me it’s interesting to see how DVR/TV streams work 
But I’m still stuck with the problem of, now that we know that UK Freeview can switch stream types “at will”, how is Plex handling this, both PMS and client? Only in that, I can see Chrome is not playing it back as deinterlaced and I know my Android TV isn’t deinterlacing (from the sports I watched at the weekend)… I suppose things can/cloud be worse if I start recoding a TV show early, and the adverts (in Progressive) are recorded prior to the main show starting, as PMS is then identify this as Progressive (which is what seems to have happened for the rugby match at the weekend) - does this matter? It depends on how Plex works with all of this
So…
(a) Now what?
(b) (In general) How is Plex handling deinterlacing? (PMS and Client)
(c) How does Plex handle switching between progressive and interlaced, during a single playback of a file?
(d) Does Plex monitor the content of the media file, so it can switch between deinterlace and progressive?
(e) Out of interest, why does Plex running TV shows at a lower FPS/Hz? I’m watching the same TV channel via both HDHomeRun and Plex and there is a distinct FPS difference! I’d never noticed this before! 
Here’s a link to the files I collected:
