Depends on how you checked. The directories are hidden. You can get to them through
Using the Finder’s Go menu, select Go To Folder… then enter the following in the dialog box that pops up:
~/Library/Logs/Plex Media Server/
I think that looks ok with read, write, execute for owner, for group and for others
Are you able to cd to it?
Also try this to see what has been created
ls -al ~/Library/Application\ Support/Plex\ Media\ Server
Looking at the logs - there is some evidence of multiple instances of Plex Media Server app running at the same time - make sure it does not show in Activity Monitor before relaunching
Nov 16, 2018 23:34:56.853 [0x7000099d9000] ERROR - HttpServer: Error binding acceptor: Address already in use
Nov 16, 2018 23:34:56.853 [0x7000099d9000] ERROR - Error: Unable to set up server: listen: Address already in use (N5boost16exception_detail10clone_implINS0_19error_info_injectorINS_6system12system_errorEEEEE)
Another example here - server exited but it took a while to shutdown
Nov 17, 2018 01:16:34.506 [0x7fffafbb6380] DEBUG - Shutting down with signal 0
Nov 17, 2018 01:16:34.506 [0x7fffafbb6380] DEBUG - Ordered to stop server.
It was still running 5 seconds later
Nov 17, 2018 01:16:39.507 [0x7fffafbb6380] WARN - Timed out waiting for server to finish.
Yet - you started a new instance of Plex Media Server.app at 01:16:36
Nov 17, 2018 01:16:36.005 [0x7000045e5000] INFO - Plex Media Server v1.13.9.5456-ecd600442 - Apple Mac - build: darwin-x86_64 macosx - GMT 00:00
Nov 17, 2018 01:16:36.005 [0x7000045e5000] INFO - MacOSX version: 10.13.6, language: en-GB
Nov 17, 2018 01:16:36.005 [0x7000045e5000] INFO - Processor Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz
Nov 17, 2018 01:16:36.006 [0x7000045e5000] INFO - ./Plex Media Server.app/Contents/MacOS/Plex Media Server
and resulting in failure because two instances were running
Nov 17, 2018 01:16:36.148 [0x7000048f7000] ERROR - HttpServer: Error binding acceptor: Address already in use
Nov 17, 2018 01:16:36.149 [0x7000048f7000] ERROR - Error: Unable to set up server: listen: Address already in use (N5boost16exception_detail10clone_implINS0_19error_info_injectorINS_6system12system_errorEEEEE)
So double check activity monitor - kill off any stuck processes before launching again
Even on next launch - it looks like some python processes were still running from earlier attempt to run the server
launched at 01:16:41
Nov 17, 2018 01:16:41.223 [0x70000c4b2000] INFO - Plex Media Server v1.13.9.5456-ecd600442 - Apple Mac - build: darwin-x86_64 macosx - GMT 00:00
Nov 17, 2018 01:16:41.223 [0x70000c4b2000] INFO - MacOSX version: 10.13.6, language: en-GB
Nov 17, 2018 01:16:41.223 [0x70000c4b2000] INFO - Processor Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz
Nov 17, 2018 01:16:41.223 [0x70000c4b2000] INFO - ./Plex Media Server.app/Contents/MacOS/Plex Media Server
but it found some residual process from earlier
Nov 17, 2018 01:16:41.365 [0x70000c7c4000] INFO - Killing process: Plex Plug-in [com.plexapp.system] (pid: 531)
This lurking process (PID = 531) was still there from an earlier launch at this time
Nov 17, 2018 01:16:29.271 [0x7000053d3000] DEBUG - Starting plug-in /Applications/Plex Media Server.app/Contents/Resources/Plug-ins-ecd600442/System.bundle.
Nov 17, 2018 01:16:29.272 [0x7000053d3000] DEBUG - [com.plexapp.system] Setting plug-in to always running (daemon mode).
Nov 17, 2018 01:16:29.272 [0x7000053d3000] DEBUG - Starting file watcher for com.plexapp.system
Nov 17, 2018 01:16:29.273 [0x7000053d3000] DEBUG - Plugin: not setting user token for plugin
Nov 17, 2018 01:16:29.274 [0x7000053d3000] DEBUG - Spawned plug-in com.plexapp.system with PID 531
These errors indicate it was failing to create or access this path
"/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins"
First attempt to access (or create it if it does not exist)
Nov 16, 2018 23:36:12.932 [0x70000dbe1000] WARN - Warning: ex: boost::filesystem::last_write_time: No such file or directory: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins", couldn't check file: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins"
After this it should be there
But still not there or not accessible
Nov 17, 2018 01:16:29.267 [0x7000053d3000] WARN - Warning: ex: boost::filesystem::last_write_time: No such file or directory: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins", couldn't check file: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins"
and again after this
Nov 17, 2018 01:16:41.369 [0x70000cbdc000] WARN - Warning: ex: boost::filesystem::last_write_time: No such file or directory: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins", couldn't check file: "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-ins"
May be that individual directory has wrong permissions / ownership
See if this shows anything
ls -al ~/Library/Application\ Support/Plex\ Media\ Server/Plug-ins
The Plex DLNA Server logs show similar issues with directories
/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/
or
``/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/`
Nov 16, 2018 22:40:29.317 [0x7fffa902a380] ERROR - Couldn't rename file "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna-new.db-shm" to "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna.db-shm": No such file or directory
Nov 16, 2018 22:40:29.317 [0x7fffa902a380] ERROR - Couldn't rename file "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna-new.db-wal" to "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna.db-wal": No such file or directory
and same later on
Nov 16, 2018 23:39:13.021 [0x7fff9fa54380] ERROR - Couldn't rename file "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna-new.db-shm" to "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna.db-shm": No such file or directory
Nov 16, 2018 23:39:13.021 [0x7fff9fa54380] ERROR - Couldn't rename file "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna-new.db-wal" to "/Volumes/Data/Users/Tom/Library/Application Support/Plex Media Server/Plug-in Support/Databases/com.plexapp.dlna.db-wal": No such file or directory
Could you get screenshot of activity monitor to show which user account the Plex Media Server and other plex processes are running in
This must be what is causing the problems
I presume you have already checked the steps you followed
There is step by step guide here - for example
and another here
There is nothing obvious from the logs - all pointing to permissions type of issue