New issue with CB field Query Drop down and CB Core field ajax Integration

It might actually be better to just add a Custom HTML field below your query select field then use CB Conditional with a Query condition to check if they've joined any events

Yes that's a possibility but I thought that displaying an empty field with an explanation about how to use it was better.
After all, CB itself offers the ability to display or not empty fields in its main settings, so why not query fields also ?

How could I add a custom HTML field below the query one and only display it during edition of the first query field and only if it's empty ? either by ajax or by profile edition ?

Where were you displaying this information to begin with? In the layout? So they'd see an empty select input with a description below it? That just feels like bad UX to display the empty select. The only way I can see to workaround this is under the Global tab of your query select add a custom blank value. Example as follows.

Value: (leave empty)
Label: - Select Event -

How could I add a custom HTML field below the query one and only display it during edition of the first query field and only if it's empty ? either by ajax or by profile edition ?

Create a Custom HTML field then add a Query condition for it to check if they'd have any options available so that the Custom HTML field only displays if there are no options. Next in the ajax settings of the query select field add your Custom HTML field to the "Additional Fields" parameter then set "Additional Field Titles" to "1 Line without Title".

The only way I can see to workaround this ....

Exactly what I needed and I did not even think at it

You're right for the UX but we have cbif statements taking care of the guidances.

Create a Custom HTML field then add a Query condition

You think it's better to have another custom HTML field or to leave it to CBIF in the query field description ?

You think it's better to have another custom HTML field or to leave it to CBIF in the query field description ?

Personally I think it's better UX to have it as a separate descriptive field, but it's entirely up to you. You'll just need to be sure the select can't be truly empty if you want it always visible if you still want to use your current usage.