I use exactly that Chromebook and here is my optimized setup after trying several options. I use it as my daily on-the-go laptop.

I run Devuan with Runit. Anything that uses SystemD is going to be too slow for this little 2 core Chromebook.

I set it up with F2FS (follow the debian howto) instead of EXT4 in an attempt to prolong the life of the little internal SSD.

I did the minimal install and then installed only Enlightenment as the desktop. You will not find a better and less resource consuming DE.

The GUI Apps:

• Terminal: Terminology
• Writing: Abiword
• Spreadsheet: Gnumeric
• Email: Thunderbird but set to leave all mail on the server and not sync any folders locally. This save the tiny SSD space and also makes it faster.
• Media: Audacious and MPV
• Web: Firefox, it runs ok but big PWAs like Gmail are very very slow.
• Smolweb: Bombadillo, but everything else works great too.
• Network: ConnMan, this is all you need, no dhcpcd etc to manage network/wifi connections, and there is a nice simple GUI "gadget" for it included with Enlightenment

I love this specific chromebook, I have the blue and white one, its keyboard is so much better than it should be for the price.

I keep a 128G EXT4 sd card mounted at /home//data and I replace dirs that get a lot of use like ~/Downloads with a symlink to the sd card.

You can squeeze a little more juice out of the CPU by changing the default kernel command line to include turning off all the CPU security mitigations. You don't need them on a single user chromebook anyway.

edit: formatting

eta: I forgot to mention that I also mapped all the top row keys onto functions in Enlightenment so they do what you expect them to do.

eta: ConnMan

honestly the distro is not going to make much difference unless you go to some special distro that runs off the ram (instead of the ssd) like tinycore or porteus

the de/wm matters most actually, in this case i'd recommend icewm, xfce or lxde.

i3/sway in Manjaro/CachyOS or just install it on raw arch/debian

AntiX Linux has been the most efficient distro on my netbook. You gotta be okay without systemd though. For the most part I didn't need it but some things are highly dependent on systemd to work.

WattOS was good too but AFAIK it's not actually open source so I couldn't trust it.

Any lxQT based desktop will be fast on low end devices. Try Linux Mint LxQT edition

I have not used it at all, so I cannot speak for it, but look into Puppy Linux.

Maybe puppy linux? Its very light on resources.

The last "tiny linux" that I used was BunsenLabs. That was for a netbook, though. No idea about Chromebook compatibility. https://www.bunsenlabs.org/

If you're constrained by the user's "tech level", it's unlikely that you'll find anything significantly lighter ... some other distro might shave off 50MB of RAM, but if it's more difficult to use, that's not really worth it.

Try OpenBSD. It's not Linux, but its RAM requirements are perfect.