Not answering your question directly, but a possibly useful workaround:
Note that iTerm respects the xterm control sequences (See
https://www.xfree86.org/current/ctlseqs.html under Operating System Controls, Set Text Parameters) - I don't believe there are terminfo entries for these.
In any case - that provides for independently setting window and tab title -
```
# Zsh print - adjust as necessary
# Set the tab title to the current named directory
print -n "\e]1;${YOUR_TAB_TITLE:?}\a"
# Set the window title to the git info (or empty) from above
print -n "\e]2;${YOUR_WINDOW_TITLE:?}\a"
```
- Robbie