Checklist

• [ x] I have tried restarting my IDE and the issue persists.
• [x ] I have read the FAQ and my problem is not listed.

Tell us about your environment

• ESLint version: 9.34.0
• eslint-plugin-vue version: 10.4.0
• Vue version: 3.5.21
• Node version: v20.19.4
• Operating System: Windows 11

Please show your full configuration:

{
...
 rules: {
 "vue/component-api-style": ["warn", ["script-setup"]],
 }
}

What did you do?

<script lang="ts">
import { defineComponent } from "vue";

export default defineComponent({
 // iPhone 6 Mockup
 name: "PhoneMockup",
});
</script>

What did you expect to happen?
Lint to fail due to component export in the file when only <script setup> is supposed to be enabled.

What actually happened?

Code passed linting.
It appears detection work based on there being a "setup" or "data" member on the exported component to determine which api is being used, with <script setup> detection being the default case as opposed to an actual detection. Because this component only defines a name, no specific api is detected, so it passes validation even though it is not using <script setup>.

I verified that adding a "setup" or "data" member to the component does cause the rule report correctly that the api being used is not allowed.

Repository to reproduce this issue