A few quotes from the Rabbi on 'Torah Study'
in which he teaches that not even a Halachic matter should be recounted during the Torah Reading
A question concerning the Haftarah. What we read from the Prophets on Sabbaths and Festivals following the Torah Reading that we call the Haftarah – what reason is there to call it the Haftarah and not Prophets? – Inform us, and be recompensed by heaven…
One reason, attributed to Rabbeinu Tam, of blessed memory, that concerning the reading of these sections we say, 'Once the Torah scroll has been opened, it is forbidden to recount even a Halachic matter', follows what has been said: 'And when it was opened the entire nation stood'. Following the Torah Reading they are permitted to talk…
So despite what Maran Beit Yosef, of blessed memory, wrote in the name of our Rabbi Yerucham, of blessed memory, who wrote that it is forbidden to speak during the Haftarah reading of the Prophets before its conclusion, just as in the case of the Torah Scroll, since fulfilling the commandment depends not only on the reader but on all those present… it appears seems that generally speaking it is considered to be forbidden, but from the purely Halachic point of view it is permitted. Which is not the case for the Torah scroll, where even a Torah matter is forbidden. And this is simple.
Yad Eliyahu, Part A, question 25, p. 25a-25b, Zion Press, Jerusalem, 1930