Behaviour of Dijkstra in Case of Negative Edge Weight
The article on Dijkstra's algorithm at GeekForGeeks say "Dijkstra’s algorithm doesn’t work for graphs with negative weight edges in general."

Introduction to Algorithms by Corman et al. says "Dijkstra’s algorithm solves the single-source shortest-paths problem on a weighted, directed graph for the case in which all edge weights are nonnegative."

As explained in the linked question and answer and as OP has found, the general proof of the correctness of Dijkstra's algorithm will fail if there are negative edges, hence discussing Dijkstra on graphs with negative weight edges doesn't make sense.

I would advise you to stay away from Dijkstra’s algorithm when a graph that has negative weights appears. It might work in some cases, but it may lead you into troubles that will be avoided if you apply Bellman–Ford algorithm or Floyd–Warshall algorithm.

By the way, the shortest distance from $A$ to $G$ is 2.