I’m a bit surprised by your budget. For something just running plex and next cloud, you shouldn’t need a 6 or even 3k system. I run my server on found parts, adding up to just $600-$700 dollars including (used) SAS drives. It runs probably a dozen docker containers, a dns server, and homeassistant. I don’t even remember what cpu I have because it was such a small consideration when I was finding parts.
I’d recommend keeping g your synology as a simple Nas (maybe next cloud too, depending on how you’re using it) and then get a second box with whatever you need for plex. Unless you’re transcoding multiple 4k videos at once, your cpu/GPU really don’t need much power. I don’t even have a dedicated GPU in mine, but I’m basically unable to do live 4k transcodes (this is fine for me)