Observations:

Cross platform network issues are constant for PlayStation users. (rarely ever see the server show up with out manually entering the share link)

LAN doesn't seem to have issues with this.

Displayed Messages:

There are no messages, the server just wont display in the list of available to join.

updated

 
Summary:
Tested today (week later), same issue. PlayStation just wont utilize the Xbox companion, which handles the Minecraft account, (least seems that way that PlayStation and Xbox wouldn't get along any ways...)

Realms seems like a service on PlayStation plagued with Minecraft Cross play issues.

Actions Taken To Repeat:

Set up realms on Windows 10, have PlayStation user on same LAN, but internet bound to connect to realms. Xbox and PC on same network connect fine. PlayStation will usually result in Realms service UN-available.

Expected Result:

That PlayStation App would act the same as Xbox does.