You could try to get a used Dell Wyse 5070.
If you pick the right dual ranked RAM modules (e.g. Patriot PSD416G26662S), you can have a max. of 2x16 GB.
There’s a slot for SATA SSDs onboard and with the right adapter (PCIe A/E key -> M key) you can plug an NVME SSD in the WiFi PCIe slot, which gives plenty room for storage and even allow for a disk mirror setup.
All that is very well within your budget and quite a beast that once was meant to be just a thin client.
Yes, it’s small, runs at a few watts and is silent.
The Celeron J4105 and Pentium J5005 CPUs in the Wyse 5070 are very close to each other both regarding energy and computing power.
Have a look here: https://www.cpu-monkey.com/de/compare_cpu-intel_celeron_j4105-vs-intel_pentium_silver_j5005
I would take either.
You’ll have a hard time finding another silent box with such a small footprint that’s able to take 2 gumstick drives - even if one of them needs some tinkering - and 32 GB RAM.