Is the aforementioned dream, which includes the girl's brother asking why the dreamer is in their house, and his mother answering that he came to propose to his sister, and the brother saying, "Then let us prepare from now for summer," considered good tidings for what the dreamer will embark upon after the Istikhara prayer?

The sign that the matter for which one sought guidance (istikharah) is good, is its facilitation and realization. One does not rely on visions or dreams to proceed or abstain. Rather, the Muslim goes forward with what they sought guidance for, and if it is facilitated, then it is good. If it is not facilitated, Allah will turn it away from them to what is better for them.