How to determine which topology a BJT is configured to from a given circuit diagram?
The three basic configurations (CE, CC, CB) don't cover all possibilities but they are essential to quickly determine the behavior of a circuit.

The configuration is always determined with respect to a given input and given output and therefore depends on the signal path that is being analyzed.

The determination of the type of configuration is actually quite simple. The name of the topology is determined by the node which is at AC ground, that is the node that carries no signal.

We have to start by identifying the input and the output of the single transistor circuit, which already excludes two terminals. The remaining terminal determines the name of the configuration.

For example a CE configuration has the input at the base (we exclude the base), the output at the collector (we exclude the collector), so that only the emitter remains. Hence, we have a CE configuration.

Might sound like a strange approach but works very well.