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.