I would like to get some cheap and extremely-portable notebook, like those 10" netbooks in late 2000s.
What's the current equivalent of such kind of devices ?
Of course I'd like to run GNU/Linux on it.
It does work. Sometimes it's failed to start and required a reboot, but nothing more than that. crostini comes standard (enabling it is just a setting). It is a Debian install in an LXD container running XWayland, so transferring her Firefox tabs and logins, thunderbird email and Libre Office documents was just an rsync. It worked perfectly, despite the old machine being amd64 and the new one being aarch64. The Linux GUI programs even appear in ChromeOS's launcher, so it's pretty seemless even for my wife. For her the only confusing aspect is the native file system and the Linux one are different trees. But that's not a problem for me, so software wise no complaints.
On the hardware side, positives are Google demands Chromebooks have 8 years of software upgrades, and I think a minimum of 10 hours of battery. My wife's gets 12 hours. The hardware is typically targeted at schools, which means robust with some models having a water proof keyboard. The negatives are you really need to spec it the same as a laptop, so min 8GB RAM and 128GB SSD, but models with those specs are rare.
If I could easily get one with 16GB of RAM and 512GB SSD it would be very attractive, but there is literally nothing like that available new were I like. And while the lower speced Chromebooks targeting education sector are remarkably cheap, the same can't be said for the higher end models when new. Second hand is a different matter - the one I did get was 8GB/128GB and cost $300. It feels a little sluggish (usable, just not snappy), and possibly it running out of resources is why it hang during installs. Or maybe that's the ARM CPU. An i3 or even N100 seems like it would be better. A Snapdragon X might even provide a mac like experience when the time comes.