I'm hosting on a Synology, but not transcoding.
It's likely more affordable to host a second jellyfin server on a desktop that is used for transcoding vs getting a NAS with the hardware.
As also mentioned you may not need to transcode unless you want to down mix to reduce bandwidth when not home. For those cases I would recommend you use handbrake and have multiple versions of the content at different resolutions/codecs as needed. Yeah it's work.
The majority of issue I have when running locally is audio codec compatibility. So I use ffmpeg to reencode and remux my mkvs with the new audio stream. (Typically eAC3)
Is this windows 11 and up or windows 10 as well?