From my understanding, files cannot be directly stored only in a timeshift snapshot – they must be first stored on the disk and only then timeshift can make a backup inside the snapshot. But I have never used timeshift myself, maybe I just completely misunderstand how it works.
Give testdisk a go, see for example this tutorial. It is a terminal utility, so it might take some time to get used to it. But no one can guarantee that it will successfully recover anything, the deleted files stay on the disk only as long as they are not overwritten.
Do you have any idea why the files disappeared after reboot? One thing that comes to mind is that they might have been saved in /tmp, in that case I believe recovery would not be possible.
Regarding to which files you should recover, try all of them and see if you have any luck.
Good luck with recovering the files!
This also seems to be great for low-bandwidth mobile connections. The advantage over reader mode here is that only the plain text is sent and not all the images, large styles and scripts…