Who is responsible for choosing a TLS cipher suite - the client or the server?

The client sends only what ciphers it supports in the order of their preference. The server then selects one of these ciphers - which means only the server ultimately decides which cipher gets used.

It is fully up to the server which cipher suite gets selected from the offered ones, i.e. the server might take the client preferences in account but might also completely ignore it. In fact, many servers have a configuration option which allows the server to use either the cipher preferred by the client or the cipher preferred by the server.