Heart rate zones higher than power zones?

Your issue is likely from using max heart rate to set your zones. Using the maximum heart rate model, you are relying on statistical averages as to where heart rates will distribute themselves by zone. Given that you are new to training, your fitness level is unlikely to fall within those statistical means. The best practice for setting your heart rate zones is by using Lactate Threshold Heart Rate (LTHR). Pretty much every fitness software is capable of giving you zones around that zone. The premise is that it is personalized to you. It is using your heart rate at your current fitness to establish zones that will more accurately approximate the strain you will incur during different power outputs.
The gold standard method of testing your LTHR is to do a warmup then ride as hard as you are able to pace yourself for 30 minutes (treat it like a race but don’t start too hard and completely fall apart). You then take the average heart rate over the last 20 minutes of that test - using the last 20 minutes helps to evaluate your true steady-state plus cardiac drift/aerobic decoupling which should not be averaged with your first few minutes of fresher legs and settling in. If you are struggling to pace that type of effort and do workouts with steady efforts at your FTP (at least 5 minutes) you might be able to get a rough estimate from those as well by looking at where your heart rate peaks and plateaus in those efforts, but testing is definitely preferred.
As you would expect, when your fitness improves, not only will your FTP increase, but you will find that the heart rate you can tolerate will increase as well. Your LTHR will go up and your heart rate at different zones will come down at the same time which will keep your heart rate zones more closely paired with your power zones. There may still be some decoupling, especially later in the workouts as you continue to build your fatigue resistance, but you won’t see immediate mismatches as your zones will be more appropriately set.
Much like a ramp test, your LTHR should be reevaluated every 4-6 weeks in your first year to 18 months of cycling. Eventually, you will hit something close to your genetic potential and that number will remain pretty stable for a long time with slight attrition for age and may drop with protracted periods away from training.

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