Looking for API to Toggle Switch in App Embeds Directly via REST or GraphQL API

Hello Shopify Team,

We are looking for a REST or GraphQL API that allows us to programmatically toggle a switch in the theme, specifically within App Embeds.

Could you please let us know if such an API currently exists, if there are any references available, or if there are any plans to release this functionality in the future?

Please see the attached image for your reference.

Thank you,
Viral Mandaliya

As far as I know, there is no such API. @Alan_G Do you have any guidance