How do I access Custom Fields in a theme component?

You could try something like this:

<script type="text/discourse-plugin" version="0.8.27">
let currentUser = api.getCurrentUser();

if (currentUser) {
        api.container.lookup('store:main').find('user', currentUser.username).then((user) => {
        console.log('user', user.user_fields);
    });
}
</script>

See Using the PluginAPI in Site Customizations for details about the "text/discourse-plugin" script type.

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