Apple Intelligence and Siri are still separate (though Apple like to make it look like they are fundamentally intertwined). You can turn Apple Intelligence off and leave Siri on for CarPlay.

How did you turn Siri off in the first place? That's where I'd start...

Settings -> Apple Intelligence & Siri:

Talk and Type to Siri -> turn all this back on

Allow Siri When Locked -> turn this back on