Should a mourner change his place at the Shabbat table?

Should a mourner change his place at the Shabbat table?

The custom is not to change one's place anywhere except in the synagogue.

Written in the Gilyon Maharsha, Siman 293: "And he does not sit in his place. Both in his house and in the synagogue." This implies that one should change his place even in his house. However, in Chochmat Adam, Klal 167, it is written: "In the second week, he goes out and does not sit in his place, both in the synagogue and in his house (this is implied by the language of the Gemara and all the poskim, although in the Jerusalem Talmud (Moed Katan, Chapter 3, Halacha 5) it is stated that in the second week he enters the synagogue and does not sit in his place, one can say that this refers to the synagogue, but in our Gemara (Moed Katan, page 23a) and in all the poskim, the synagogue is not mentioned at all, and if so, it is obvious that it refers to all places, he does not sit in his place and does not speak, but reduces his speech). etc. "And in any case, it seems to me that although I wrote that he does not sit in his place, this applies even to his house, but regarding the twelve months, certainly, one should not be stringent, as I have never seen it practiced even in his house in the second week (and also in Rashi around Alfasi (Moed Katan, page 14, column 1 in the Vilna edition) it is clearly explained that he does not sit in his place in the synagogue, therefore one should not be stringent about this at all even in the second week, only in the synagogue, and certainly not for all thirty and twelve months for his father and mother):" And the custom follows Chochmat Adam.