There's a reason why you aren't seeing a lot of information on Chromebooks running DAWs. While there are DAW programs that are supposed to run on Chromebooks, such as BandLab and SoundTrap, they are browser based programs. As such, you're somewhat limited by factors such as internet speed and storage.
I haven't been a fan of the Chromebook. It seems to be perfectly fine for functions like word processing, basic spreadsheeting, web browsing and email, their capabilities are limited. To me, it's like trying to run the Daytona 500 with a Toyota Corolla. It's a great car for going to work, the grocery and going on vacation, but high performance isn't it's forte. For serious recording, a decent PC is much better equipped for the task.
I would suggest that you give a rough idea on available funds. Then it will be easier to see what basic system you might be able to build. Something like a refurbished laptop with an I5 processor, 8GB RAM and an SSD can be had for $200-250. An interface like the Behringer UMC202HD or 404HD will run you $70-150. Those two items, along with your microphones and headphones will get you started for hardware. The only other thing you would need would be a DAW, of which you could either go with something like Cakewalk by Bandlab, or Reaper.
The other option would be to go with a self contained unit such as a used Zoom R16 or R24, used Tascam DP24SD, DP-03, or DP-08. You can get them for the $200-300 range, depending on the unit and if it's new or used. They have advantages in that they are portable, and generally easy to setup and get recording. With a bit of reading of the manual, they are almost plug and play. The deficiency is that they are more difficult to work with in terms of editing and mixdown, but it can be done to the point that you have a finished 2 track song.
What might work for you is to do the recording into a portable self contained unit, and then transfer the files to the Chromebook for mixdown (or basic PC). I have done this with good success. I have a Zoom R24 and once things are recorded, I simply pull out the SD card and transfer the files to my PC for mixing and editing. As I said, they are very portable, so if you go to a friend's house, you can take it along, plug in some mics and record. Even the very basic H4n from Zoom or Tascam DR40x can do 4 channel multitracking. You can get used units under $100-150. For dirt cheap, you CAN make pretty decent recordings with them.
The only way to truly know if the Chromebook DAWs will meet your needs is to try them out. You should be able to run them and find a song with a few tracks online, and see if you can get them mixed and if things run smoothly. If you need some files, just ask. I'm sure we can get you tracks for your testing.