Peripherals are one thing, handling concurrent streams, transcoding… is another one.
So in theory, a Pi can be kept alive with a power bank, but OP is expecting (as I understood) multiple hours of streaming (with “local” only access) , which includes the above tasks for multiple concurrent streams. How big of a power bank we’re talking about and how long will it last?
As others already wrote, I would go with the Plex server at home and using the “Download” feature to have some content available offline for the times you don’t have internet. You can actually set a limit for the size of the download library and individually set video and audio quality for the files.
Seen raspberry pi mentioned some times, I don’t have one, so maybe I’m wrong, but I don’t think there would be an easy way to power it up on a train for example.
I still think you should give this one a try. Unless, you’re goal is not like having an actual solution, but doing this project as a hobby, and throwing some money at it. Which is also fine, I’ve done the same before.
Testing one or two of these media severs will cost you some hours of your time. Anything other will take much more time, effort and money.