The parallelism here where Giyuu motivated Yae to live, hunts him now (karma). So I think there is a high chance Giyuu married Yae, coz the author opened the arc here where Giyuu is very depressed knowing of his time limit, but Tanjiro in the extra stated he looks more motivated now in the current letters. So Karma happened, might have been a moment where Yae is the one to motivate him. Also, I think he got depressed after his Hot Springs vacation with Uzui (who flirts with his wives). Its not hard to imagine since Kanao and Yushiro are both working for a cure.
The parallelism here where Giyuu motivated Yae to live, hunts him now (karma). So I think there is a high chance Giyuu married Yae, coz the author opened the arc here where Giyuu is very depressed knowing of his time limit, but Tanjiro in the extra stated he looks more motivated now in the current letters. So Karma happened, might have been a moment where Yae is the one to motivate him. Also, I think he got depressed after his Hot Springs vacation with Uzui (who flirts with his wives). Its not hard to imagine since Kanao and Yushiro are both working for a cure.