This appears to be an issue with the command prompt additions that Extraterm makes in the setup_extraterm_zsh.zsh file.

If I comment out these two lines, the problem goes away:

extraterm_install_prompt_integration
add-zsh-hook precmd extraterm_install_prompt_integration

Update: narrowed it down to this line:

prefix=''`echo -n -e "%{\0033&${LC_EXTRATERM_COOKIE};3\0007%}%?%{\0000%}"`

If you change that to prefix='', the problem goes away. So it’s definitely something that’s being added to the prompt that’s causing it.