I grabbed an ASUS E210 about a year ago and it's doing great with Linux on it. It's fanless, with an 11.6" display, 4G of ram, a 1.1 Ghz celeron, and 64G of storage. You can get one dirt cheap as an ex display model. I don't know if it's still up, but there was a surprisingly good repair manual for it on the ASUS web site, showing in detail how to install an m.2 storage device, so I souped it up with an additional 8TB of storage, which I'm using for jellyfin, immich, calibre, and paperless-ngx. It will just about manage to run a virtualbox vm if you need to do any windows stuff.

With laptops, there’s no match for the thermal efficacy of the MacBook. That’s why you can only find laptops with mobile CPUs. If you buy a Mac to run Linux, get an M1 or M2. Be aware of the caveats (not all features are supported). With any laptop, you could in theory undervolt the CPU and screw up the fan curves to make it effectively fanless.

If you are ok with a mobile CPU, a lot of chromebooks are fanless and you can slap Linux on them, but they’re slow.

I'm very fond of my Pixelbook Go. They are not new but still can be had at a somewhat decent price: https://www.amazon.com/dp/B07YMM4YC1

It's fairly simple to get it running Linux via this project: https://docs.chrultrabook.com/

The screen is 165.63 PPI, nearly what you're looking for. It's plenty crisp and clear for me at 1,920 × 1,080.

And most importantly, it's thin, fanless, and the battery is decent.

I'm thinking about getting a used MS Surface-like tablet with a keyboard cover instead of a laptop. Seems that it might check your boxes, too.

Yes. The Apple Silicon Macbook Airs. That is it.

I'm not an Apple fanboy, but I am a fan of silent/efficient computing (and personally own Apple, AMD and Intel computing hardware that qualifies in that category) and it is shocking and weird that Apple is the only real silent/efficient/HiDPI player in the laptop space.