I cannot hold down my homescreen to change wallpaper

Have you changed your Wallpaper since you updated to iOS 16?

If no, then you need to change this the first time here:

Settings → Wallpaper → Add New Wallpaper.

You should then be able to change your wallpaper from the Lock Screen by holding your finger on the screen.

You can find more useful information here:

Change the wallpaper on your iPhone - Apple Support

Yes. The wallpaper you had before iOS 16 cannot be used in the new wallpaper setup. Therefore, it must be set up the first time in settings.

You're welcome.