The Shield may not be powerful enough to transcode 4K HDR video in real time, especially if HDR to SDR tonemapping is required. HDR to SDR Tonemapping is performed in software on the Shield. It cannot take advantage of hardware acceleration (using the GPU).
The FireTV Stick 2nd Gen does not support 4K video (Fire TV device Specifications).
You’ll need a FireStick 4K to direct play 4K HDR video. A FireTV Cube 2nd gen may work as well, based on its specifications.
Regarding the remote location:
Successful remote playback depends on available bandwidth. Both the uplink speed at the server location and the downlink speed at the remote client must have enough bandwidth to handle a 4K stream.
You will also need a 4K HDR capable client. I’m not sure if the Fire TV 3rd Gen (pendant) can play 4K HDR video. I have a 1st gen cube, which has similar specifications, and it cannot playback HDR video via Plex (despite the specifications showing HDR10 support).
You can monitor playback via Plex Dashboard → Now Playing. It will show if the media is direct playing, direct streaming, or transcoding.
This thread has useful information regarding playback of 4K video using Plex: [INFO] Plex, 4k, transcoding, and you - aka the rules of 4k
