can Admin give any user "install any program" without giving them the Admin role?

Is "install any program" the only function of Administrator? What other functions are unique to Admin?

In order to give install any program to a user, must I give them the Admin role? Is there a switch I can throw that will allow this action on user's part without having to give them the login PIN for Admin?

Not sure, but I kinda think you would have to turn off UAC to do that.

I know that you can do what you need in the Server version of Windows 11, it may be possible in the Pro version too, but i would doubt the option is there in Home versions

The way to achieve the control is to create a new user group, or modify an existing one - you need to add the install All option to the group

I have Windows 11 Pro and found these settings in Group Policy, gpedit.msc. Computer Configuration\Administrative Templates\Windows Components\Windows Installer. There is a policy in there called 'Always install with elevated permissions'. It says, This policy setting directs Windows Installer to use elevated permissions when it installs any program on the system.