The Qing is a Manchu dynasty. You'd think they'd want Outer Manchuria back much more than some uninhabited parts of Tibet that Britain could just as easily give them anyway.

Also, China has given no indication that it's joining Britain and France as much as it's becoming a co-belligerent the same way that the United States and France simultaneously fought Britain in 1812.

Chinese participation in The War of the Alliance With a Silly Name isn't as grand as you seem to be making it. China isn't selling its soul to Britain or France.