Agree that HR is misleading, I don't even wear the strap anymore. Without a PM, Cadence is only useful if it's the same route, drag conditions and gearing. Thing about cycling is our bodies want to do it efficiently. If that means our brains can trick us into thinking an RPE of 6 is really an 8 then it will.
All breathing patterns tells us is how we're doing at that moment based on atmospheric conditions, effort, fitness, hydration, comfort, mental state, etc. Comparing that to speed, cadence, time or anything else is kinda pointless.
Which is why a PM helps because Cadence (angular velocity) is part of the power formula. Knowing two numbers (applied power and angular velocity) helps when adjusting the third (torque) and now everything makes sense. If you put out 240 watts at the beginning and at the end of a long ride and you're breathing easier then that would be a phenomenon. I'm guessing that's not going to happen. GL