GLP-1 drugs seem to increase resting heart rate. I suspect that also increases total daily energy expenditure, although I don't know that we have reliable data on that yet.
That can happen, but is not universal. My resting heart rate has been dropping (probably in lock step with my weight), it has not risen one bit since I started taking tirzepatide. And my heart rate variability has been trending up, not down.
Why do you suspect it changes energy expenditure?