That you see the clients connected to the HP switch on the Meraki Dashboard isn’t unexpected. Every client at some point - especially if it’s Windows - will broadcast traffic across the network and so the Meraki switches will ‘see’ it, since the HP switches will forward the broadcast everywhere. As expected these appear on the uplink port just like you describe.
What does surprise me is what you say regarding the visibility of traffic and applications. Under normal circumstances you wouldn’t expect traffic on the HP switch to be forwarded to the Meraki MS unless it was destined for a client there. Unless anyone has a better idea all I can suggest is that for some reason the HP is acting as a hub and just forwarding all the traffic it sees to the Meraki MS. This might be a bug in the HP firmware/code, or a configuration error on he HP, or it might be ‘designed’ behaviour for a trunk (if you’re using a trunk), but whatever it is, it sounds like the HP switch is misbehaving.