tmux 3.2 and above provide the copy-command option to set a command to pipe text to copy. You will also need the wl-copy command from the wl-clipboard package. Add the following line to your ~/.tmux.conf:
set -s copy-command 'wl-copy'
As of writing this post, tmux 3.2 is only available in experimental, so you’ll need to install it from there:
$ sudo apt install -t experimental tmux