Switching between cells will cause a latency spike, and a lot of correlated packet loss if the subscriber has a large queue of undelivered data, but that's all. But handling packet loss and ordering are what TCP is supposed to do.
I have no idea of what you mean by "the TCP connection is no longer there". The TCP connection is a distributed system living on the client and the server. It doesn't go away unless one of the endpoints decides so. (Modulo stateful middleboxes, like NATs. But nobody in their right mind would run a TCP state-aware middlebox on a cellular network base station).
IP changes are relevant when switching networks entirely, like going from WiFi to mobile.
One type of roaming that does trigger for smartphones and similar devices is WiFi->4G/5G->WiFi.
You're at home, obviously you don't want expensive mobile network data charges when you've got WiFi. So the connection is over WiFi. But as you walk out the door, currently your application software needs to spot that the WiFi is going away (not too hard), connect over the mobile network (unless your policies say to give up instead to save money) and keep going. QUIC would allow this to be done transparently at the transport layer, at least in some cases. When you reach a coffee shop/ friend's place/ work and there's WiFi again, the opposite transition saves you money and if you go indoors and signal is weaker may also be necessary to deliver a working network.