This has been a great resource for verifying compatibility before you put money down on anything, granted you don't require the latest bleeding edge parts.

Ryzen 2200G / Athlon 200GE?

Quoting: ageresRyzen 2200G / Athlon 200GE?

That's a good lead, thanks. Successors 3200G and 3400G also seem to fit a fanless build. And Vega 11 seems pretty powerful.

gigabyte has a huge lineup of different small factor pcs if you don't want to build it yourself

https://www.gigabyte.com/Mini-PcBarebone

(but I can't find ryzen builds though)

but I did a quick search on ebay and for 424 usd you could buy this ryzen 2400G small factor pc https://www.ebay.com/itm/AMD-Ryzen-Mini-PC-ASRock-A300-HTPC-AMD-Ryzen-5-2400G-8GB-DDR4-250GB-SSD/274029325245?hash=item3fcd6babbd:g:qXoAAOSwXtFdg24q

for a little more you could buy this one with 16gb of RAM

https://www.ebay.com/itm/PC-linea-OFFICE-AMD-RYZEN-5-2400G-Ram-16-GB-DDR4-SSD-480-GB-Windows-10-Pro/133177046596?hash=item1f01f87644:g:M64AAOSw5nZdXUz5

(but both of them not fanless though)

Yeah, fanless is my main focus there. GB has only two or three fanless brix and I couldn't find them in the stores anyway.

well and what about this https://www.phoronix.com/scan.php?page=article&item=compulab-fitlet-i&num=1

looks sweet for 385 at amazon but you have to get the ram and disk separate though.

here's a nice DIY build of a ryzen 2400G https://www.youtube.com/watch?v=9XaAr7E9-tk

it's just a matter of getting a passive cooler and the build would be just what you are looking for.

but searching more deeply turns out that for a 2400g you'll need a better cooler like the one they are using at this build

https://www.youtube.com/watch?v=nrvyWpisYmE

the No Fan CR 80 E

Not only brand new, but also you could consider secondhand items, based on your low specifications. I've been very happy with a number of small form factor Mini PCs, such as Intel NUC, Asus Vivo, Gigabyte Brix, MSI Cubi. (I've been able to get Debian, Mint, Ubuntu and *coff* Windows) working on all the ones I've used (i.e. minimal driver issues).

Not only are these all very small indeed, using up minimal power, but tend to have features which are desirable in such products, such as built-in Wifi, Bluetooth, HDMI port, multiple USB ports, RJ45 network socket. I like that they tend to be easy to open, fit a NVMe SSD and/or 2.5 inch SATA SSD/HDD, usually fit one or two sticks of SO-DIMM RAM.

Some of these do have little fans in them (and some are fan-less), but those fans tend to be much quieter than full-size PCs.

Thank you all, and especially @guest, for valuable input. Based on your comments and some further reading, I eventually ordered:
Intel NUC 8 (NUC8i5BEK)
Crucial 500GB M.2 PCIe NVMe P1 + heatsink
2x Kingston 8GB 2400MHz CL17 1,2V (probably 8GB would be enough but since it's so cheap...)
All that for around ~$500 + VAT

Now, while NUC isn't fanless, I've read that the noise in series 8 is significantly lower than in previous models and shouldn't exceed 40dB, so I decided to try. Worst case scenario I'll pass it on the kids and keep looking (or I could probably switch the case for Akasa Plato X8 or Turing, or some such).

Other options I've considered was building a box using a passive miniITX case and Ryzen 5 (but the case I liked the most - Silverstone PT13, seemed impossible for a passively cooled build, and most of the others were either out of stock - like HDPlex H5 - or hard to get), and at the other end of the spectrum I briefly pondered on ordering a fanless (and nameless) i7 8565U build from aliexpress.

Also @guest
1. I didn't want another laptop as I've already had many and I was never entirely happy, so I wanted something different.
2. I actually have Raspberry Pi 4 but I don't think it would suit my needs. Particularly I'm not sure if everything I need would work on an ARM processor.