Plex is a bit of a problem when it comes to reverse proxying, exponentially so when it comes to subfolders instead of subdomains. I cannot recommend enough just putting it on a subdomain instead. It wants /web, /system, /servers, /accounts, /myplex, /photo, and /clients, as far as I’m aware.
That said, here is a very pertinent guide which covers using nginx for this purpose, the approach should be the same for Caddy with some config reverse engineering.