bug#41531: 27.0.91; Better handle asynchronous eldoc backends

[Eli Zaretskii]

> From: Dmitry Gutov <dgutov@yandex.ru>
> Date: Wed, 8 Jul 2020 21:32:33 +0300
> Cc: 41531@debbugs.gnu.org, Stefan Monnier <monnier@iro.umontreal.ca>,
>  andreyk.mad@gmail.com
> 
> Both Stefan and Eli were too busy to do an in-depth review.

Actually, busy or not, I did the best review I could.  I'm sure Stefan
did the same.

And next time you'd like to know whether I did an in-depth review or
was too busy to afford that, you can ask me.