If you install a portable version, then the library is also maintained in the installation folder.
This would mean, if I interpret your setup correctly, that you have to install MP3tag as portable version on your NAS.
But this would mean that you are now limited to the network speed for access.
As a reminder I would like recall this thread about the purpose and function of the library:
If you access your collection on the NAS with various MP3tag installation, then in general each installation treats the files like an individual installation.
And a word on
Mp3tag is no collection management program but a tagging program. For the management of collection there are dedicated programs which may grant a faster access to individual files - provided, external changes are synchronized with the internal presentation in these managers. And this synchronization will probably be not much faster than MP3tag reading the files.