I’m having the exact same issue and with a Suunto 9 Baro, supposedly their flagship watch of a few years back. It’s not a heart rate strap issue. Before starting the activity the heart rate reading is accurate, the moment I start the activity the reading is 35% odd lower. The moment I pause the activity, the reading is accurate again.
Have you found a solution? It’s driving me mad. I feel let down by Suunto.