Cycling is power referenced to HR, so yes, having a power meter outside is really really useful. For example you said climbing to maintain cadence, well, if the grade is slowly increasing, your power is increasing to maintain cadence. Sometimes I get overly excited before hard intervals, and can see HR slowly increase due to excitement. Sometimes a car comes close and my HR shoots up. Generally my HR is stable relative to steady power, but there are exceptions both indoors and outdoors. Hard to say anything with the info given. Hope that helps.
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