What events count as a state transition?

What can cause the “state transitions” count of a workflow to go up? Is it more than just adding events to the history?

Each update to your workflow execution state is called a state transition and it to the most part corresponds to a db update.

Here is (most likely incomplete, but hope it helps) list of updates that add towards state transition count:
Start workflow / child workflow exec
Completion of workflow / child workflow exec
Cancelation (workflow / child workflow / external / activity)
Activity exec
Activity retry
Activity heartbeat
Local activity exec
Side effect
Workflow sleep
Upsert search attribute
Signal
Timer create
Timer cancel