Maybe it was that Merkel just didn’t want to do state visits.

It’s possible she didn’t for the French president she had to deal with. As far as I remember she got along with Chirac, but for a short time, she despised Sarkozy, she didn’t care much for Hollande and she was quickly disappointed by Macron.

First state visit, not first visit. A state visit is something particular with all the honours and the like.