Important Update: This answer is outdated. I'm leaving in place for historical purposes, but most users should read my updated answer for the latest (and more important) information.
wsl --update in Windows 10 only updates the WSL2 kernel, not WSL itself. That's not really going to add any new WSL "features" such as GUI support. The only new feature that is purely enabled through an updated kernel is USB/IP support.
In Windows 10, the WSL version is (currently, at least) locked to the Windows release. Since Windows 11 has come out, we're honestly not sure if future Windows 10 releases will receive new WSL updates. Some indications that I've seen are that the 22H2 Windows 10 will have minimal changes, but we just don't know yet.
To run GUI applications using WSLg, you'll have to upgrade to Windows 11. Microsoft has explicitly said that it is unlikely that they'll be able to bring this functionality back to Windows 10.
Alternatively, you can use a third-party X server or XRDP as in the answers to this question.
Note that under the released WSL on Windows 11, wsl --update behaves the same -- It only updates the kernel. However, Microsoft has provided a "Windows Subsystem for Linux Preview" that is available for Windows 11 users (only) in the Microsoft Store.
This WSL version is updated independently of Windows releases, so Microsoft (and users) can try out new features and fixes more often than the once-a-year Windows cycle.
In the Preview version, a wsl --update will update to the latest WSL Preview release.
There are a few limitations with running WSL as a Store app, so it's not clear to me if Microsoft will be able to resolve those, or if the Preview version will remain a "rapid release" channel with the Windows update gaining the "Stable" version once a year. It's also not clear if Microsoft will be able to bring the Store version back to Windows 10 at any point, but it seems unlikely.
Error: 0x8024500c
That error indicates an issue contacting the Microsoft Store, so it's likely that the kernel update feature uses a Store (or at least UWP delivery) mechanism. If you can't update via the Store, then you may not be able to use --update either.
However, there are several other ways to update the WSL2 kernel under Windows 10:
If your organization has set it, the "Receive updates for other Microsoft products when you update Windows" option (In the Settings -> Windows Update -> Advanced settings) will automatically obtain the latest WSL2 kernel release when it is available.
I'm assuming that you don't have access to change this setting yourself, if your user permissions don't include the Store. It's typically an IT-managed setting.
You can try downloading the kernel update as an .msi directly from Microsoft per the "Manual Installation" for WSL page.
Note that if you can't run the installer directly, you can probably still extract the kernel from the .msi and point to it via .wslconfig (see here for the kernel setting).
If all else fails, you can download the latest source release of the WSL2 kernel from the Microsoft GitHub repo, build it, and then point to it via .wslconfig (as per the previous option).
(Insert obligatory, "In my day, we had to build the kernel for every device change ... uphill ... both ways.")