One could perhaps set something up to forward a connection to a local daemon and then use that forwarded connection to push data backwards, but the complexity is going up, and fast.
ssh -R 127.0.0.1:2210:127.0.0.1:22 user@somemachine
Of course you could instead add it to your ssh config along with agent forwarding. ssh user@host "cat foo.txt" | pbcopy
from my Mac terminal.> One could perhaps set something up to forward a connection to a local daemon […] [but complexity]
You can make some headway with this, but it's a bit painful. You need some fixed presence on the Internet, somewhere, like a server. That can be done, but now you're setting up routing, etc. Or paying Tailscale. It rubs me a bit of the wrong way, since the ISPs job was to provide end-to-end connectivity, and ISPs as a whole are falling down on that … I shouldn't need to build a shadow network in the IPv6 private space …
(And again, we breach the "it isn't worth it" complexity barrier for a cross machine clipboard transfer…)