Oh, Plex. Bless you for trying to move beyond your customer base that serves huge amounts of pirated video, I do hope you succeed (I say this sincerely as a lifetime pass holder).
An aside but I do find it darkly comic that we're now streaming retro games. The ROMs are at most a few MB big but this service will burn through that in seconds.
My assumption based the note that Linux Plex servers won't work with Parsec is that the emulation & streaming is done on your local network.
Either way, I've yet to have a suitably positive experience streaming anything interactive on either LAN or WAN. I see the improvements that have been made and many friends swear by it, but it may just be that I'm too sensitive to input lag and even the rarest encode/decode hiccup.
Which have you tried? I had similar problems as you with steamlink, but geforce experience+moonlight has been a godsend. Works incredibly well (if you have a Nvidia GPU)
Steam has been the only thing I've tried LAN (other than some early PS4 remote play years ago), so that may be the issue. Geforce Now is probably the best I've tried of the bunch, so I'll give their tools a shot locally next time.
An aside but I do find it darkly comic that we're now streaming retro games. The ROMs are at most a few MB big but this service will burn through that in seconds.