I’m still having this issue too. For me neither signing out of the app and signing back in, or exiting the app and reloading it update the content list.
Strangely if I add movies they appear immediately but TV Shows only show in the On Deck section so I have to click and hold on them to watch them as they don’t show under the series.
TV: LG OLED65CX5LB (Software v03.23.35)
LG Plex app: Client v5.25.2 / Platform v5.2.3
Plex server: v4.54.5 (running on unRAID)