I’ve no experience w/ Chromecast devices. Others can help with those.
Regarding the desktop, you don’t mention which Plex client you are using.
Use Plex for Windows. It direct plays most video and audio, including 4K HDR. It scales 4K to 1080 if needed. Note that HDR is tonemapped to SDR. Plex for Windows does not send HDR to the display.
Plex Web is limited by the browser. HEVC video transcodes, no tonemapping, most audio transcodes. Useful for server administration. Not so much for playback.
GPU
Is this the Kepler based Titan?
If so, it does not support HEVC decoding, so will be of little assistance when transcoding 4K HDR media.
You need a Pascal or later based card to decode 10-bit HEVC media (a GTX 1050 or later).
See Nvidia Encode/Decode Matrix for capabilities of their cards.
Edit: Note that Nvidia GTX cards are limited by Nvidia to three simultaneous transcodes. It is possible to exceed the limit via modified drivers. See Elpamsoft for information on Nvidia transcode performance and obtaining the modified drivers.
CPU
The QuickSync graphics in the i6-6400T cannot decode HEVC 10-bit video.
It does decode HEVC 8-bit video. Plex Media Server can use it to transcode non-HDR HEVC, H.264, VC-1, & MPEG2 video.
Edit: Note that Plex uses either the Nvidia or the QuickSync graphics for hardware accelerated transcoding, whichever is chosen as the primary video handler for the system (a BIOS setting on some systems). Plex cannot use both at the same time or fall-over from one to the other. Plex falls back to the CPU if the GPU is not available.
The CPU is not powerful enough to transcode 4K video by itself (w/o hardware acceleration). It has a 4417 Passmark. It can transcode 2 x 1080 streams, but a 17000 Passmark is needed to transcode 4K HDR media. See What Kind of CPU do I need for my Server?
Is my media Direct Playing, Direct Streaming, or Transcoding?
Monitor playback via Plex Dashboard.
Is my GPU used when transcoding?
You can use the console instead of digging through the log files.
See this post for details. Cross reference the output with the Tech Specs table in the Hardware Acceleration support document to see if the video is transcoded on the CPU or the GPU.
Transcoding 4K HDR & Tonemapping
Reference: HDR to SDR Tonemapping
Turn off HDR tonemapping in Settings → Transcoder (show advanced if needed).
Tonemapping is not supported on Nvidia w/ Windows, so it will hit your CPU instead.
Tonemapping is compute intensive. I have not seen hard data posted regarding CPU requirements, but it is likely your CPU is not powerful enough, even if the video is transcoded on a GPU.
Basically, you can add a GPU to transcode 4K video, but you’ll have to wait for Nvidia support to get HDR → SDR tonemapping
Additional Info
[INFO] Plex, 4k, transcoding, and you - aka the rules of 4k
Help us help you - how to provide logs to get your problems identified and hopefully resolved
