The physical form factor is still around today, if you want a notebook PC that's smaller than an ultrabook.
Current flag carrier is probably the GPD P2 Max from Sheznhen's Gamepro Devices, a firm who started out making linux-based handheld game consoles around 2013 then branched out into netbooks. The first GPD Pocket stuck a maxed-out version of the Intel netbook spec sheet in a machined aluminum body with a 7" screen (underpowered processor and all) but newer models include less underpowered devices. In particular the P2 Max has the same footprint as the Eee 701/901 models but is thinner and lighter -- at 650 grams and 1.4cm thick it's comparable to an iPad mini with a keyboard -- thanks to the metal unibody construction.
https://gpd.hk
There are also competitors from elsewhere, notably One Netbook's One Netbook A1, which can be ordered with either an RS-232 port or gigabit ethernet if you work in a data center and want a portable terminal:
https://1netbook.com
Both companies also do tiny gaming portables with Windows 10/11 and the ability to drive an external GPU.
So basically the netbook sector is alive and well, if yuo want something significantly smaller than an ultrabook.
Finally, if these models strike you as too pricey -- they're not aiming at the same price point as the Eee -- there are less powerful variants on the theme from Chuwi and various nameless Chinese vendors. Just poke around on AliExpress for a bit and you can find a 440 gram micro-laptop for a reasonable price (if you don't mind waiting a lot).