(How) can firebase hosting be used as reverse proxy?

Question

Tools like posthog require to setup a reverse proxy to be used properly, and with Vercel for example, this can be easily done with :

{
  "rewrites": [
    {
      "source": "/ingest/:match*",
      "destination": "https://app.posthog.com/:match*"
    }
  ]
}

(How) can I achieve the same in firebase hosting? I tried rewrites and redirects with the following configs, without success...

    {
      "source": "/ingest/**",
      "destination": "https://app.posthog.com"
    },