I have the apple watch. I like it. One thing it has on it is the heart rate monitor. When I'm exerting, which can be walking around my house, my heart rate will go up. It goes up even further if I exercise. That's normal. However, your heart rate does sound high. To just be walking through your house, you are getting to the heart rate level of someone doing cardio exercise. What is your resting heart rate? Is it high? I agree that these wearables aren't always accurate and don't tell the whole story. But what I do like is that I can see my recurring resting heart rate and charts say that's in a good range. :>) The other thing that I always look for is recovery. I may run up my stairs and my heart rate goes high but does it go back down pretty quickly?
Anyway, I would mention it to your doctor. According to the package insert for Effexor and sites that list side effects, increased heart rate is a side effect. https://www.healthline.com/health/venlafaxine-oral-tablet. Risk to benefit ratios take place when side effects happen. Is it enough to warrant trying a different med? That's between you and your doctor. Let us know what they say.
It does change when you stand. It does change when you move about. Constantly checking your heart rate when you have no reason to suspect you have a problem might be a problem, though. Also, those devices like Fit Bit aren't loved by cardiovascular specialists. They can be wrong. They can be used incorrectly. You might just once check your pulse with your fingers the old fashioned way. If you have any real concerns, such as one would have if they had a heart problem, then you would need to see your doctor. Although Effexor is a stimulating antidepressant and could cause agitation, I don't know that it would be reflected in your heart rate, and as your resting heart rate is normal, you're probably fine.