Can installing older DirectX on Windows 11 mess up the system?

No, it will not mess up your system but there is no point to doing it.
On the other hand, the OTHER STUFF in that pack I make no guarantees about.

Microsoft has code in Windows to block old (Microsoft only) installers that aren’t compatible with the system.

In addition to this, the dxsetup program also checks versions.

This post on Microsoft communities will point you to the version I just installed in my Windows 11 VM.

If you run the installer, it will check the versions.. ask Microsoft if there is a newer one, and look very busy probably doing nothing.. it might add functionality but I seriously doubt it. I checked the versions supported AFTER running the installer and it is the same as before.

The directX install appears to be pointless so why even risk it?
It appears that A vanilla Windows 11 already has support for DirectX 9.

Run “dxdiag.exe”
Move to the “Display” tab and home in on the Drivers group. Specifically, you will be looking at the “Feature Levels” line.
Scroll down to the end of the line and you will see that you already have support for DX9. This list looked the same before and after running the installer.