Possible to turn off prevent cross-site tracking for a web app that has been saved to home page?

My team has developed a Glide app (web app, not a native iPhone app) that can be saved to the home page and accessed like an actual app. In our Glide app, we have an embedded other app, that requires the Safari settings to allow cookies and not prevent cross-site tracking in order to work. When these settings are turned on for Safari, and users access our app in Safari directly, the embedded app works fine. However for the users who saved our app to home screen and access it that way, even if they allow cookies and turn off prevent cross-site tracking in Safari settings, the embedded app does not load. Is there any workaround for this? If not Safari, what browser is the "app" that has been saved to the home screen using? Why does it have separate settings from normal Safari?

Possible to turn off prevent cross-site tracking for a web app that has been saved to home page?
 
 
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