Updated server application, now remote access doesn't work

Did you get that version from Synology’s App Center?
Try installing a recent version from Plex’s download page (using the option to manually install it).

IIRC, versions between 1.42.3 and 1.43.2 had a security issue and are not able to connect by any app remotely.
https://forums.plex.tv/t/important-security-update-for-plex-media-server-v1-43-2-and-earlier/942319