There should be a setting in BIOS for sleep state that lets you choose between "Windows sleep" and "Linux sleep". I know I have to set that to "Linux sleep" on my P14s gen 2 AMD or it wakes up immediately after going to sleep. Updating BIOS and the other firmwares might help too.

However I have a gen 7 from work running Windows that often fails to wake up from sleep or hibernation, and I have to resort to poking the reset button to get it to respond. Coworkers report similar troubles so I think it may be a cursed model.

That said, I'm running OpenSuSE Tumbleweed KDE on my P14s and an X1 gen 5. Everything works smooth out if the box on both machines except for the fingerprint sensor on the gen 5 which doesn't have mainline fprintd support in any distro.

You could try fedora KDE spin or opensuse... But not sure if changing will fix these issues

Did you check if there is a bios setting related to suspend, and that it's set properly?

I have an X1 gen 9 and sleep-on-close worked just fine with Fedora for the time I used that distro (although it was KDE, not GNOME). Every other distro I tried worked as expected in that respect.

I have been having the same issue with a Lenovo laptop but on NixOS. I suppose this is a kernel issue; I'll try updating and see if it solves the issue.

1. you're likely describing hibernate not suspend suspend has different states and the most common one is suspend to ram which needs a low concurrent supply of power and that's on all laptops the default - certainly on all thinkpads I own
2. check the systemd configuration file for your close lid actions such as suspend
3. hibernate means the machine is completely off and only works if you installed the OS in a specific way (please search how to install fedora to do this)
4. fedora is not superbly newbie friendly, maybe try ubuntu, linux mint or popos which usually work out of the box

I don't think any distro supports the X1 Carbon better than Fedora. My previous work machine was a 6th gen, and Fedora worked great on there, including power management and suspend. The only thing that didn't work was the fingerprint reader, but that has been resolved in more recent models. Starting with the 8th gen, Lenovo sells them with Fedora pre-installed. Lenovo works directly with the Fedora project to ensure their hardware works correctly. As others have mentioned, the most likely problem is something misconfigured that is stopping you from suspending. You could try updating the firmware and possibly resetting it to the defaults (although check through each setting to make sure nothing is set to be Windows-specific). You might also try a fresh install of Fedora to see if it was an OS-level misconfiguration.

P.S. There is no such thing as Fedora 38.5. The project only has major versions, not minor versions.

Try another Kernel.