The HP Microservers in my opinion peaked at Gen8. Gen9 went back to fixed components and Gen10 just isn't in competitive in todays market.
You shouldn't be so quick to dismiss the mini PC's though. Something like the linked below would be a quarter of the power draw and I've linked you a CPU comparison, a higher model like an N305 is about a 200% increase on the Ivybridge CPU you mentioned as well as having good HW offload capability if you choose media serving.
CPU comparison
Even the N100 which is last generation now (superseded by the N150) beats the 3470T if that helps show where your expectations are compared to what's available.
A basic ugreen DXP2800 comes with an N100 and is ready to go although I personally wouldn't go head first into the ugreen os. The 4800 adds more disks and more performance to that mix.
You've mentioned you want to run on it, one of the small form units is perfect for your use case, my previous reccomendation of a £400+ unit didn't acknowledge your usage and I assumed you'd be running multiple dockers and maybe a VM and so on. Music store and serve, cheeky video serve maybe? N100/N150 or machine of that ilk is going to be everything you could ask for and it'll do it quieter, faster and cheaper than building on ancient hardwre.
Your budget is really good for what you want, you could happily pick up a unit and a 4TB NVME to go inside and have some change leftover.
Finally... As I'm starting to go on. Don't be scared to build or use a desktop PC. You may have built gaming PC's but that's not what you are trying to build here. A preloved HP Prodesk with an 8th Gen i5 would be the entry point, can be picked up for <£200 and give you easily double the performance of a Microserver, enough storage configuration and you mentioned power draw, they sit at about 30w idle (similar or less than a microserver). Gaming PC's are power hungry because they always want mooooaaaarrrr FPSz, a quiet little box in the corner serving content does not need to do this.
My main home server (hogwarts - don't ask) is an elitedesk 800 g4 which does all of the everythings for me, try as I might to justify replacing I can't.