bug#52389: 29.0.50; Imenu does not pop up the Completions eagerly

[Juri Linkov]

>> I think the safest way to solve this long-standing problem without
>> surprising users is to introduce a new variable whose logic is handled
>> correctly, and mark imenu-eager-completion-buffer as deprecated.
>
> Sounds good to me.  (The new variable could be an alias of the old name,
> but have a name with the opposite meaning, and then things would
> continue to work for everybody.)

This is a good opportunity for generalization.
Like there is icomplete-show-matches-on-no-input,
would it be possible to create a new user option
e.g. minibuffer-auto-show-completions, and allow
to customize what commands should use it.
Then it could be like completion-auto-select
recently proposed by Philip.