>> 1. the current buffer should remain the same for the next command;
>> 2. the buffer-local value of 'default-directory' should remain the same;
>> 3. the next command should have a new value of 'default-directory'.
>>
>> I see no way to satisfy all these requirements.
>
> Except adding a variable like 'project-current-directory-override'
> somewhere inside 'command_loop_1'.

And indeed with the following patch replacing the current definition of
'project-switch-project' with just:

  (defun project-switch-project (dir)
    (interactive (list (funcall project-prompter)))
    (setq next-default-directory dir))

'C-x p p (select project ...) RET M-& pwd RET' confirms that
the command runs in the selected project directory.
Whereas the original buffer keeps its previous buffer-local value
of 'default-directory'.