Can't connect securely via app.plex.tv when on the same network as Plex server

Secure connections not working in the local network is virtually always an issue related to DNS.
Set your DNS server to that of Google (preferably in the settings of your router or wherever your DNS resolver operates) 8.8.8.8 and/or 8.8.4.4

Tell the DNS resolver to not block the domain plex.direct from re-assigning local hosts: https://support.plex.tv/articles/206225077-how-to-use-secure-server-connections#toc-4