I haven't really played around with that much, sorry. I don't typically use sleep on my laptops. I prefer to either hibernate or just shutdown and start up again when I need it.
I'd guess that the X13s hardware support in Ubuntu is likely as good as Debian, and switching probably wouldn't help you much. I have noticed that newer kernel versions (notably 6.12 and later) and the latest firmware (as of sometime last year) really fixed a lot of little issues for the X13s. That probably makes a bigger difference than the distro. I'd check to see which versions you're using.
I'd guess that the X13s hardware support in Ubuntu is likely as good as Debian, and switching probably wouldn't help you much. I have noticed that newer kernel versions (notably 6.12 and later) and the latest firmware (as of sometime last year) really fixed a lot of little issues for the X13s. That probably makes a bigger difference than the distro. I'd check to see which versions you're using.