Thanks for the reply. Plex Media Server is removed from your system.
Now try to re-install.
The DS415+ has an Atom 64-bit CPU, so you want the Intel 64-bit, DSM 7 version of Plex.
Use the PlexMediaServer-1.29.2.6364-6d72b0cf6-x86_64_DSM7.spk file that @ChuckPA previously posted here (the second link of the three you listed above).
Make sure the file name matches exactly. No (1) etc like Windows places on duplicate downloads.
Perform a manual installation using Synology Package Center.
The Atom C2538 is a very low power CPU. It may take some time for the installation to complete. Let the process run to completion. Do not interrupt it.
After the installation is complete, you should be able to claim the server.
From a system on the same network as the NAS, point a private/incognito browser window at the IP address of the Synology. The private window bypasses any browser plug-ins that might interfere.
For example, if the NAS’ IP address is 10.1.2.3, use http://10.1.2.3:32400/web.
Do not click the “open” button in Syno Package Center, use a domain name, Synology Quick Connect, etc. You must use the IP address to claim the server (it is a DSM 7 thing).
Give it a try and report back how things go.