Keep in mind that the Bracha is not usually required. AIUI, the only two Torah Mitzvos (as opposed to Rabbinic) where the Bracha is required are Birkas Hamazon (Grace after meals) and Birchas Hatorah (the blessings said both as part of morning blessings and before/after reading an Aliyah/Torah reading). In the case of Birkas Hamazon, the Bracha is the Mitzvah. In the case of Birchas Hatorah, the Bracha is a Torah requirement, though there are failsafes - e.g., the Bracha before Shema is generally considered a substitute when necessary. In all other cases, the Bracha is an "extra' - e.g., if you don't make a Bracha before blowing Shofar or before eating Matzah, the Mitzvah still counts. So while in many cases there are reasons to repeat a Bracha based on time elapsed/interruptions, if not repeated the Mitzvah still counts - i.e., you would not repeat the Bracha + Mitzvah based on "Did the Mitzvah but the Bracha was no good".

Thanks manassehkatz‭; I did not know that. So the b'racha might not be required for the mitzvah to count, but don't we still have to worry about a blessing made in vain? If you say the b'racha and don't do the mitzvah, either "at all" or "in time", haven't you made a b'racha levatalah?

Bracha Levatalah is a real issue, and so the question is quite relevant (and which is why I am only commenting, as I don't have the actual answer). So planning properly in terms of minimizing time/interruptions between Bracha and Mitzvah is quite important. But in the end, if there is a delay/interruption (however that is Halachically defined) that invalidates the Bracha for that Mitzvah but you did the Mitzvah anyway (presumably because you didn't realize the delay/interruption was a problem, but could also be for example if one person is making the Bracha and someone else is doing the action - which can definitely be the case with Shofar when the Baal Tokeah has already fulfilled the Mitzvah and is now blowing for someone else and the other person makes the Bracha) then the Mitzvah counts.

Still just comments, but a little more info: Just started studying Mishneh Torah Hilchos Brachos. In introductory, mostly general, rules, mentions that a relevant interruption is not a Hefsek - classic example is "pass the salt" between Hamotzi and eating bread (Mishneh Torah actually has this example, but I have heard it elsewhere as well). Arguably "page numbers" would fall into that category. I think generally accepted is that additional discussion not required - e.g., a Dvar Torah about the Torah or Haftorah - would be considered a Hefsek citation needed. That being said, I am pretty sure that historically Akdamus was recited after the Kohen said Birchos Hatorah but that now (at least in all Shuls I know of) it is recited after the Kohen is called up but before he says Birchos Hatorah.