New Tzitzit during the Thirty Days of Mourning

Is it permissible for a mourner during the thirty days to buy a new tzitzit if the old tzitzit appears worn out?

Since he has a tzitzit to wear, it is forbidden to wear a new tzitzit, and it is not permitted to wear a new garment even if it has tzitzit. And since it is for the purpose of a mitzvah, let someone else wear it first.

In She'elat Ya'avetz, Part 1, Siman 82, it is written regarding a new tzitzit on Shabbat during the week of Tisha B'Av: "Nevertheless, it seems to me that if he has no other tallit at all, and it is impossible to borrow, so that he has a tzitzit at least during prayer, it is permissible, for certainly they did not decree in such a case, as it is uncommon, and it is better than one who has only one shirt which they permitted for bodily needs. All the more so for the needs of the soul's garment. And since anyone who reads Shema and prays without tzitzit is as if giving false testimony, it is better to make a new garment to fulfill the mitzvah. But if it is available for prayer time, he should not make it, even if he goes all day without tzitzit. And he is like one excommunicated to Heaven, in deliberate matters this is said. And this is compelled by the decree of the sages, and it is better not to annul their decree, since they do not punish for a positive commandment, and in such a case there is nothing to worry about, and since it is not a personal obligation, why should the decree of the sages not stand in its place, as it seems to me, Ya'avetz, s"t." However, in Rav Pe'alim, Part 4 - Orach Chaim, Siman 29, it is written about him: "Behold, in this matter we do not follow him, and his words are not clear at all, because in truth, in all such cases, when it is a matter of a mitzvah, the sages did not decree a prohibition at all, and as we find in several things that are forbidden in the days after the fast, and they permit in the place of a mitzvah, all the more so in such a mitzvah, when he is deprived of the mitzvah of tzitzit, going all those days without tzitzit, for this does not bring healing, therefore it is clear and simple that even in the case mentioned by Rav She'elat Ya'avetz, z"l, which is a new garment, without which he is forced to go without tzitzit, it is permissible to fully wear a new tallit, and there is no annulment of the sages' decree here, because even in such a case they did not decree at all, and this is clear. And see there that he even permits wearing a washed tallit for the mitzvah. And apparently, according to his view, when the tallit is worn out, it is considered a mitzvah, as explained in Rashi "This is my God, and I will beautify Him", "make for yourself a beautiful tallit". And as written in Mishnah Berurah, Siman 24, s"k 9. In Shulchan Aruch, Siman 389, Paragraph 1, it is written that the prohibition of new clothes is only for seven days, and in Paragraph 2 it is written to forbid a white and new garment, as explained in Moed Katan 17: and in Rema, Siman 389, Paragraph 3, it is written that the custom is to forbid twelve months for a father and mother, and thirty days for other relatives, even for colored garments, and we do not find in the poskim a permission to wear new clothes on Shabbat.