Rework example section

[strzibny]

This PR reworks the example section to be more direct and simple. Based on the internal discussion and part of the clean up for our integration pages (see issue 8336). If you think we should add outputs for each sample, we could do that. It's a reduction for clarity, but we can still decide to feature more later.

[trusche]

Thanks @strzibny, overall a good improvement, I think.

It's a bit surprising though to not lead with a plain Google example; by far our most popular engine. Immersive product is currently first in your example, that's pretty specialised and requires a prior request to fetch a token. I'd move that one way down, or even exclude it. I'd rather see more of a spread highlighting the breadth of our APIs. The old list was getting a bit long indeed, but it did have much more variety.

[strzibny]

The idea with skipping Google search is that it's already mentioned before in a 'quick example' so repeating it feels wrong when we have so much more to mention. Still, it's not a replacement for documentation, so we can significantly reduce the examples. I am completely fine with not including Immersive product first given the extra token. On the other hand having this more complex example can be helpful. But I think I agree with you that it shouldn't be a first example. If we would keep it, what position would you assign to it?