Thanks for asking this question!
Battery is one of our top most concerns and we work hard to optimize Google Fit’s battery usage and provide a magical experience.
Google Fit uses a mix of sensors(Accelerometer, Step counter, Significant Motion counter), Machine Learning and heuristics to get the data right. Our algorithm is pretty similar to your 1st option plus a little bit of magic.
We periodically poll accelerometer and use Machine Learning and heuristics to correctly identify the activity and duration.
For devices with hardware step counters, we use these step counters to monitor step counts. For older devices, we use the activity detected to predict the right number of steps.
Our algorithms merge these activities, steps and sometimes location to correlate and further increase accuracy.
We do not poll GPS to estimate steps or detect activities.
— Engineer on Google Fit Team.