Transcoding occurs on the Plex Media Server, not on the TV. Synology NAS generally have lower power CPUs which struggle with transcoding video (You don’t mention your specific model).
Using a Shield with an appropriate AVR or soundbar works very well for Plex.
When using the Shield with an AVR, the preferred connection method is:
Shield <-- HDMI --> Receiver/Soundbar <-- HDMI-ARC --> TV.
The reason for connecting the Shield (or any streamer box) directly to the receiver is HDMI-ARC cannot pass lossless audio such as TrueHD or dts-HD. It is limited to AC3 5.1, EAC3 5.1, dts 5.1, and PCM 2.0. TOSLINK Optical/Coax has the same restrictions as HDMI-ARC.
Make sure the receiver/soundbar supports all desired audio formats and also passes 4K HDR video. The key audio formats to look for on a spec sheet are: dts-HD MA; dts:X, TrueHD 7.1, and TrueHD + Atmos. If the AVR supports those formats it will support the older ones as well - AAC, AC3, dts, PCM (but double check things anyway).
My setup:
Shield <-- HDMI --> Denon 4300 <-- HDMI-ARC --> LG B7 OLED
PMS runs on a Synology DS 918+
This setup works very well for me. Everything in my library direct plays. It is rare that I need to transcode any video or audio. I have an older Shield, so it supports only HDR10, not Dolby Vision (2019 models add DV support).
