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.