One thing to understand here is that it mostly depends on the “desktop environment”, which is basically the GUI of the system. (Imagine you could have the Windows XP GUI on a Windows 11 PC. Or the macOS GUI on a Windows 11 PC.)

Distros intended for desktop use will typically come with a certain desktop environment by default, so to some degree, you can talk about the distro, but yeah, there’s just gonna be a strong correlation with their default desktop environment.

To my knowledge, GNOME and (recent/Wayland versions of) KDE have good support. Most comments here imply these two desktop environments, so for example Ubuntu, Fedora and POP!_OS are typically GNOME, whereas Kubuntu and Nobara are typically KDE.

Some folks here also mention Linux Mint and LMDE working well, which use the Cinnamon desktop environment, so I guess that works well, too. Cinnamon is somewhat based on GNOME.
Well, and Elementary OS’s whole shtick is its Pantheon desktop environment, which is also based on GNOME.

So, basically, as Elementary’s Pantheon is its own thing, there’s no guarantee that it’ll work, but I would not be surprised.
As someone else already said, you can use a Linux Live USB to try it out before installing. You should be able to just follow along the installation instructions of Elementary OS and shortly before you actually install things, you should find yourself in Pantheon and can try it out.

Yes, I run Pop_OS on my Lenovo Yoga 6, no complaints whatsoever

I use Fedora Atomic (GNOME Desktop Environment) and it works amazingly with a touch screen!

Ubuntu

Don’t use it. They apply some weird patches to make the touchscreen experience worse. Try Fedora instead.

Arch Linux on Dell 7389 : just works. Also had OpenSUSE Tumbleweed on this machine, best installer ever.

Debian on Thinkpad X390 Yoga : with included variable-pressure pen, the touchscreen is actually a wacom tablet, perfect. Also, one if the best installer there is.

Ubuntu on Thinkpad T480s : just works. Installing Ubuntu today is literally just a couple of clicks. Wife hasn’t complained in 3 years, this distro must be doing it right.

(Everything Gnome here, no additional setup whatsoever. The KDE gang will argue that Plasma has a lot of goodies for touchscreens, be sure to check it out)

I’ve been running kubuntu on a lenovo yoga for years, works great.

I think the only think is that the touch screen maps incorrectly when there’s a second monitor plugged in. I didn’t use it enough for that to be annoying, and it’s possible it’s fixed on plasma 6, I haven’t tried yet.

I’ve got a Surface Go 2 running Kubuntu and it’s been running fine. Performance overall seems to be better compared to Windows, and the touchscreen works fine as well.

I’ve experienced some kinks with the Surface Pen’s responsiveness in that sometimes drop-down dialogues won’t be properly selectable with the pen, it’s skipping options for some reason if I hover over one, so I have to use my finger instead.

Apart from that, I have an extra program for an on-screen keyboard since, for some reason, the pre-installed on-board keyboard is only available when logging on the device.

Most multitouch functionality is also available right out of the box, like pressing the screen with two fingers at the same time to simulate a right-click.

I have LMDE on an old Lenovo Yoga, but it doesn’t disable the keyboard when in tablet mode. It’s on my list of crap I need to fix. Make sure to check that behavior before you go full install.

Touchscreen works OOTB on my Dell XPS in Ubuntu and Debian.

I’ve used an Acer Spin 5 and Dell Latitude 7440 with Kubuntu, Ubuntu, Arch, Fedora and NixOS over the years without many issues.

I’ve heard that the x360 laptop you have may be a little troublesome but you can always test things out on a live Linux USB.

• I’ve heard that the sound quality might be degraded on Linux, or certain speakers don’t work
• The flip switch doesn’t work, meaning that the keyboard and trackpad aren’t disabled when flipped.

Ofc, there are a few x360 laptops so it might not apply, I’d encourage you to just give it a go with a live USB.

For using your stylus for note taking, I’d recommend trying Xournal++ and/or Rnote

I can’t see why it shouldn’t be. I have used it with touch screens. It works great. Remember that Android is linux too, and that really spurred the development in that area… :-)

Touchscreen (and 2-in-1) support in general is quite good, both Gnome and Plasma (two most popular “desktop environments”) support it well. It should be about as responsive as it is on Windows, because the response time generally comes from hardware and not software. However, I must warn you that I’ve had a similar HP 2-in-1 (although a different model) and there simply wasn’t a Linux driver for the touchscreen so it didn’t work at all; all the other tablet-like features worked fine. I would first check on a liveUSB - the touchscreen should work there the same as it will on the installed distro. If it doesn’t work, well, there’s your answer.

I have an x360 running bazzite with gnome and it runs great.

I have a similar convertible device, and it’s almost good with KDE. KDE components switch to a layout with more whitespace and bigger icons so they are easier to touch, and some KDE programs like the file manager also opens a special menu on long press on files that is an easier to use version of the right click menu.

firefox also handles it well, I can easily scroll a page with momentum, but I can also select text.

my device also has a plastic pen (no buttons or battery in it), and linux knows to ignore touch input when the pen is near the screen so that I can rest my palm on it while writing.

but a major pain point is that so far I haven’t found a real touch keyboard. there is Maliit, which is much harder to build locally than other programs, and if you get it to work it is hard to use. then there is squeakboard, but last time I was looking into it that depended on wayland protocols that were not implemented yet in KDE’s compositor

It absolutely is. I had a Dell 2-in-1 with Ubuntu preinstalled like 10 years ago.