If you’re in ST4, the hamburger menu is controlled by this setting:
// Adaptive theme only: controls if a custom or default title bar is used.
// Note that on Windows, the hamburger menu is used whenever this is
// enabled and the adaptive theme is in use.
"themed_title_bar": true,
That is, if you use Adaptive
and you want the menu, you can continue to use that theme and just turn the setting off. Other themes don’t support this setting out of the box and so switching the theme will also return the menu.
Note also that some older themes have rules for styled title bars which prior to ST4 would only have had any effect on MacOS; now that ST4 also supports this on other platforms, using an older theme could hide the menu unintentionally, in which case the solution is to either switch your theme or ask the author to update it to properly support the setting.