Is there a way to read from present tty?

In practice: I boot into tty and manually start the graphical session (Wayland/Sway). I occasionally get (non-Sway) warnings when I return to tty (eg close the window manager). But the output is always scuffed, so I can't read the whole log. The lines get printed on top of each other or something.

Is there a way to read everything from tty, from within the tty?

Neither of the methods below work, because the warnings/errors aren't produced by Sway itself, but some other OS module/component.

$ sway |& tee /tmp/sway.log

$ tail -f /tmp/sway.log