Gotcha.I think the connector is the same, the adapter cable itself is rated for different power depending on how many PCIe power connectors are on it. The one that came with the 4070 has two so would be 300W susupply.
So the headroom would still shrink when using one that comes with 2x6+2. 4070ti would be towards the top of that config with little headroom (in spec).