>>> However, point can be freely moved by, e.g., C-f or C-b., without
>>> terminating the Isearch.  This is a bug.
>>
>> This is because 'isearch-menu-bar-commands' contains 'menu-bar-open'
>> added in bug#32990 to allow invocation of isearch commands from menu.
>
> bug#32990 was a very long thread, so I didn't read that -- but does this
> mean that the reported behaviour isn't a bug?

It's still a bug.  The problem is that when the menu-bar is disabled,
menu-bar-open calls tmm-menubar directly, but in isearch-mode
isearch-tmm-menubar should be used instead.  isearch-mode-map remaps
tmm-menubar to isearch-tmm-menubar, but this doesn't help
in case of menu-bar-open calling tmm-menubar directly.

I see no way to fix this other than handling isearch-mode in tmm-menubar: