Yeah, 37Gbps sounds about right for Thunderbolt 3, so the cabling seems good.
I could be wrong, but I think when you access the internal drive of the other Mac, you are essentially accessing it over a network (even though it's a Thunderbolt network). If so, then macOS is using the SMB network disk protocol. I've read that SMB is not very efficient, and that the macOS implementation is not very "good"(?). My guess is that the slowdown is caused by this 'network drive' access with SMB.
One could rule out SMB by using 'rsync' in Terminal. My understanding is that it uses its own (faster) protocol.
IMHO, 950 MBs is not bad a performance for a network-attached drive. One shouldn't expect 2800 or 3000 MBs like you could get with a Thunderbolt 3 or USB4 enclosure that's directly attached.