Magento 2 – Change theme for product to “Magento Blank” not working – invalid template file

I try to change the theme for a product to the default Magento Blank theme. But I get this error:

Exception #0 (MagentoFrameworkExceptionValidatorException): Invalid template file: 'Company_Base::header/mobile/icons/search.phtml' in module: '' block's name: 'mobile-search'

The file Company_Base::header/mobile/icons/search.phtml is from my custom theme. Why does it even try to load a template from my custom theme if I want to load the Magento Blank theme?

Why do I get this error?

I already tried to recompile everything and clear cache, does not help.

Tested in Magento 2.4.2