"... the existence of God is not a scientific question at all.

That's correct. Such a question can not be dealt with by 'science' unless there is added in some element that also make some sort of scientific claim. "God lives atop Mt. Everest"

But, if not scientific, what kind of question is it?

*I* have been at pains to say, the very question, as stated, makes certain embedded assumptions and is 'loaded' by positing an entity and 'naming' it, THEN asking whether 'it' exists. Persons who are, for whatever reason, already inclined toward some sort of internalization of the concept referenced BY the word 'god' (especially if capitalized) will be predisposed to answer 'yes'.

It is hard to even construct any short, semi-neutral way of asking a question about the possibility of an omnipotent 'being' (already loaded) or 'entity' which was here before there WAS any 'here', and which 'decided' (a human process) to 'create' 'everything', including certain beings, in 'his' own image.

There are long, involved technical, philosophical ways of explaining the status OF such questions, but they tend to make the brain hurt without previous study of the required terms.

The point I try to make is: There is some doubt whether certain questions, while grammatically coherent, can even be asked in such a way as to elicit meaningful responses from an average set of people.
(The famous question "How many angels can dance on the head of a pin?" falls into this category... it make assumptions in its very construction and asks for speculation about metaphysics that strain the imagination)

One can ask relevant questions about personal attitudes, such as: "Do you adhere to various beliefs and moral imperatives that you understand to be supported and promulgated by the [insert one religious denomination here], based on your best guess that they have the insight and subjective coherence to justify your trust?"

Even that has weaknesses, and is not exactly something you'd see on a survey...*wry smile*

I say it this way... just because "Is there a god?" is clearly NOT a scientific question, it does not follow that it is, in that form, a meaningful question at all. Once asked, people INSERT meaning when trying to answer it, and obviously there are many varieties OF meaning, gleaned from different sources as well as from linguistic context and deeply personal concepts.
When the question(s) "Is there a god?" or "Do you believe in God?" is asked, we learn something about people, but little or nothing about 'god'......