[somat]

The way it is done is to have an invisible layer underneath (mpls perhaps) that can do the routing.

However the correct ip way to do it would to have tcp(layer 4) decoupled from ip(layer 3) such that an ip address could change while maintaining the tcp stream. unfortunately this was not done, tcp has too many layer violations and is firmly interlocked with ip. I don't know much about the state of the art, does http over udp (quic) allow for ip address change?

[wastedpotential]

Yes. Packets contain a connection identifier, so the connection can continue were it left off when the client switches ip.