At DigitalOcean, three situations, three answers. A droplet is your own server: the rule goes on its web server. App Platform does not relay a path outside the app: it needs one small service next to the site. And Cloudflare in front of it all does the job with nothing changed at DigitalOcean.
Where: the nginx or Caddy config on your droplet, for acme.com
A droplet is your own server: the rule goes in the nginx or Caddy configuration already serving your site, on the droplet. It is the nginx block described above, and it costs nothing.
Where: your app spec (Settings → App Spec), plus one small service component
Three steps: two files (package.json and server.js) in a folder of your repository, then, under Settings → App Spec, a meritt-proxy component and an ingress rule routing your prefix to it. It is a paid DigitalOcean service; the smallest instance is enough.
Where: Cloudflare (free plan) in front of acme.com
In Cloudflare: Add site, your domain, Free plan, and you point your registrar at the two name servers it gives you. Then Workers & Pages → Create Worker, the script from the app, and a route on your prefix. Nothing changes in App Platform.
On a droplet, the web server rule: it costs nothing. On App Platform, the added service is billed by DigitalOcean, and the smallest instance is enough. Cloudflare is free but moves your name servers.
Yes, with the small service: a static site alone cannot relay a path, and App Platform's redirect rule is a real HTTP redirect, not a relay.
No. Your name servers move to Cloudflare, the free plan is enough, and nothing changes in App Platform.
The click sets a first-party cookie on your domain. Your server can bind a customer id to it, and that is the level that survives a change of device.
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