HTTP/2, in my experience, still works fine on decent connections, but the advantages definitely start to level out as the connection gets worse. HTTP/2 definitely has some inherent disadvantages over HTTP/1 in those regards. (Though it depends on how much you are constrained by bandwidth vs latency, to be sure.)
However, HTTP/3 solves that problem and performs very well on both poor quality and good quality networks.
Typically, I use HTTP/2 to refer to both HTTP/2 and HTTP/3 since they are basically the same protocol with different transports. Most people don't really need to care about the distinction, although I guess since it doesn't use TCP there are cases where someone may not be able to establish an HTTP/3 connection to a server. Still, I think the forward looking way to go is to try to push towards HTTP/3, then fall back to HTTP/2, and still support HTTP/1.1 indefinitely for simple and legacy clients. Some clients may get less than ideal performance, but you get the other benefits of HTTP/2 on as many devices as possible.
However, HTTP/3 solves that problem and performs very well on both poor quality and good quality networks.
Typically, I use HTTP/2 to refer to both HTTP/2 and HTTP/3 since they are basically the same protocol with different transports. Most people don't really need to care about the distinction, although I guess since it doesn't use TCP there are cases where someone may not be able to establish an HTTP/3 connection to a server. Still, I think the forward looking way to go is to try to push towards HTTP/3, then fall back to HTTP/2, and still support HTTP/1.1 indefinitely for simple and legacy clients. Some clients may get less than ideal performance, but you get the other benefits of HTTP/2 on as many devices as possible.