Just to add to what Sidgr said, I believe 言う is/can be a so-called 瞬間動詞 (I called it stative earlier in this thread which could be misleading as that is used as a translation of 状態動詞 in the models below - I was trying to imply that once the action is done then it is always in a state of having been done). These terms are not really ones used much by natives themselves but I tried to find some resources on this topic for people to look at.
This is a very simple video explaining the basic idea in easy Japanese but with no details.
This video explains it in a bit more detail. You’ll note that some verbs are able to work as both a “regular” 継続動詞 and a 瞬間動詞. Also worth noting that a lot of materials on this topic are aimed at foreign learners or, in this case, Japanese people teaching foreign learners - it isn’t something Japanese people study in school, as far as I know.
Here is the Japanese wiki page on lexical aspect. Sidgr mentioned aspect above - interestingly it seems a Japanese linguist ( 金田一) attempted to apply the idea to Japanese and the wiki page explains his theory a bit. The same guy is mentioned in the video above as it is his classifications of Japanese verbs that we’re using here.
This is a blog post which explains 金田一’s model a bit more simply with examples etc. This is much easier to read than the wiki page although it lacks the context.
You can find a discussion on a blog about the general area of this topic (aspect and verb types) in English here, here, and here. They use the terminology of 遂行動詞 (performative verbs) which I think I have never seen used outside of that blog but their opinion seems well researched at least. It’s enjoyable to read if you are a grammar nerd anyway.
To reply to the OP of this thread more specifically, I am not sure there needs to be a lesson on the “rule” that you have brought up as it comes under the umbrella of a far more complicated part of Japanese grammar and isn’t limited just to 言う. I don’t think Bunpro could facilitate every nuance like that, especially as I don’t think it is something that comes up on the JLPT and Bunpro is a JLPT focused resource. I have long suggested a series of articles that aren’t in the SRS system that deal with nuances or larger topics. Also, if you have a further point to make then it might be best just to make it so it can be judged on its merits and not on drama