I can't find one thing regarding hrm run vs hrm tri: the materials.
I had problems with the electrods costing, they opened up on my hrm run red one (after about 1.5 years).
Now I'm asking if these parts on the Hrm Tri are the same, identical, of the Hrm run or maybe they are better assembled and could last longer?
As far as I know, those metrics are indeed only provided by HRM-Run/Tri. But you can use a separate Running Dynamics pod: https://buy.garmin.com/en-US/US/p/561205
I use a basic Garmin first generation HRM (works the best for me) and the RD pod, it works great. Advantage of the RD pod is that you also have the extra metrics when you only use the built-in optical HRM.
BTW I don't think you can transfer session heart rate stored in the H10 directly to a Garmin device (as you can do with HRM-Tri and HRM-Swim).