Incredible! I was looking for something like this since long ago.
I will test it.
When I try to add my Shlink server into my local Shlink Web Client app, it shows the following error in the web console:
Cross-origin request blocked: Same-origin policy does not allow reading remote resources at https://..xxx/rest/v3/health. (Reason: Unsuccessful CORS request). Status code: (null)
Shlink
It's running under Docker, on my server. It's publicly accessible via Cloudflare Tunnels. The docker-compose was created with the HTTPS enabled, also the domain and subdomains loads with HTTPS.
When I try to visit the service using its public address, I can see the 404 error page, and I can interact with it via cmd.
It's public domain is: https://links.my-site.com (just an example)
Shlink Web Client
It's running under Docker, on my server. But, it's not publicly accessible, but being able to connect only from LAN via HTTPS using a local certificate created with DNS Challenge. It's configured with Nginx Proxy Manager.
It's local domain: https://shlink-wc.my-apps.lan (just an example)
So, both Shlink and Shlink Web Client services are under HTTPS.
Maybe, something must to be done in Cloudflare actually?