I’m not a Manjaro user, but I am an X13s owner, and I’m paying very close attention to what’s going on for the X13s. Right now, I don’t think you’ll get much of anywhere; apparently, for one, the X13s doesn’t share certain information with EFI (I’m not sure I have this quite right) WRT the UUID for the hard disk, and this causes issues during installation. But even more important is that the kernel doesn’t really have much support for the hardware. WiFi does work, but sound/bluetooth doesn’t, graphics aren’t accelerated, etc. However, I’m seeing Ubuntu doing a bunch of development, as well as Lenovo (the former for installation-side stuff; the latter for kernel updates). I’m gonna guess the X13s is a viable platform come Ubuntu 23.10 – since they’ve already chosen kernel 6.2 for 23.04, and the bulk of the important changes are in 6.3, I just don’t see it happening by April release. However, if the installer works, perhaps an update to 6.3 would be feasible before 23.10. Hopefully other distributions pick it up, too, as I love the look and feel, but refuse to run WIndows.
Good luck!