Report to the user if some or all keywords were ignored

Does it only match those items that contain “des”, or does it match all items? What happens if you add a second keyword, one which is not ignored? It might just be that the sole keyword is stripped out of the search because it is a stopword and then the search merely returns all results. Specifically checking for this scenario has not been implemented yet, as far as I know.

Your assumtion is exact. This is precisely what happens !
I did not realise "des" returns indeed all results
"des" + a non excluded keywords returns what match out that 2nd keywords.

Do you agree this is not an expected behaviour and it should be corrected?

This is expected behavior, however, it’s clear that it’s confusing to users as there is no indication as to what’s happening.
We even collect the ignored keywords internally, we would just need to display them to the user.

Changing this to a feature request. I’m open to suggestions and MRs.
We might just want to display a warning or something? But we also might want to make this optional, as not everyone might be happy with this change. Providing a Views area plugin for this would be even more flexible, but would also make this harder to spot for admins when setting up the view. With a simple query option, we could even default this to TRUE for new but to FALSE for existing search views – in case we are worried that too many will disapprove of this change.