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Plex is overhauling its apps with a redesign and under-the-hood upgrades
(www.engadget.com)
This is a most excellent place for technology news and articles.
I can't speak for iOS but for Android the official app allows you to download the files but you have to watch them in another app. There's a 3rd party app for Jellyfin that lets you download and watch in-app. It's peak open source fragmentation.
Server transcoding is there and works great though.