There’s no way to see the complete title of the currently-playing track or album in the ‘Now Playing’ display of Plex Web. Clicking on it takes you to the Album Detail page, but there is still no indication of which track is playing.
I wonder if it depends on the browser? For at least Safari on my Mac and Edge (Chromium-based) on my PC it shows the complete track title in a tool-tip when I hover over it: