from an accessibility point of view: is it o.k to close a cite tag with a footer tag inside the blockquote like it is shown in this example https://www.thewebmaster.com/html/tags/examples/blockquote/blockquote-tag-footer-element/ or maybe 'figcaption' is more recommended? What way is the most suitable for accessibility and screen readers when creating blockquote?
I've been looking at many articles and found them contradict each other and not clear enough
The spec for blockquote gives you some guidance. It specifically says:
Attribution for the quotation, if any, must be placed outside the blockquote element.
In your webmaster example, the attribution is inside the blockquote.
The third example in the blockquote spec uses figcaption (outside of the blockquote), which you had considered. That feels like the best solution for accessibility.