How to point wildcard subdomain to some /subfolder or /path?

You can add wildcard domains on fly.io, see e.g. Limitations with respect to wildcard certs or domains per app? - #7 by Zane_Milakovic

Then, handle forward on within your application (or probably on some reverse proxy which you are using inside your image, like nginx).

as an example,

server {
    listen 80;
    server_name ~^(?<subdomain>.+)\.example\.com$;

    location / {
        rewrite ^ https://example.com/$subdomain permanent;
    }
}
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