With rust-mode-20230805.1558 from melpa, emacs 28.2 from Debian bookworm, when I'm editing a file over tramp and try to use rust-mode's C-c C-c C-t (or C-c C-c C-u) shortcuts, cargo is invoked on the local machine. In contrast, when I C-x compile cargo test, the right thing happens, i.e. cargo test is invoked on the remote machine over tramp.
With rust-mode-20230805.1558 from melpa, emacs 28.2 from Debian bookworm, when I'm editing a file over tramp and try to use rust-mode's C-c C-c C-t (or C-c C-c C-u) shortcuts, cargo is invoked on the local machine. In contrast, when I C-x compile cargo test, the right thing happens, i.e. cargo test is invoked on the remote machine over tramp.