I'm not sure this change is required at all.
Yes, you are right, I've just tried and the circular dependency is no problem. Still I prefer to think of tag manager as just one specific part of geany and not a separate library so I kept the patch. But I have no problem to remove it if others disagree.
Are their other projects that have a tagmanager or fork or has it become more or less geany-specific?
It's basically completely Geany-specific. It was originally based on this
https://sourceforge.net/projects/tagmanager/
which got abandoned 14 years ago, then picked and modified by Anjuta, then the Anjuta version got picked and modified by Geany (Anjuta dropped tagmanager in the meantime) and then heavily modified by me in the past years. So while the overall logic of maintaining tags is similar to the original one, the sources are very different. There's no living upstream version of what we have in Geany.