Somebody has made the rather arbitary (and hardcoded, boo) decision that the filename should be truncated to 30 bytes, but the path
Somebody = me. The initial implementation was in f1eb8dc22 and was requested in https://sourceforge.net/p/geany/bugs/298/. It might be a good idea to make the width configurable and by setting it to 0 to disable the feature completely. But as always, it needs someone to do it.
In the meantime, there is a right click dropdown, but with 360 files its probably not much use.
The Addons plugin also provides a toolbar icon to quickly show a list of open files though it's pretty much the same as the right click dropdown on the tar bar.