In my textbook is the following.
あの店のパンはとてもおいしいとか。今日、帰りに買って帰ります。
From what I understand, 「帰りに買う」 means "to buy on the way back (home)".
However, this seems to already imply that you are heading back afterwards. The sentence appears perhaps a bit awkward to me.
Is there anything lost if one removes the last portion and says the following instead?
あの店のパンはとてもおいしいとか。今日、帰りに買います。
Additionally, would a native speaker generally include the ending 「帰ります」, and if so, in what situations?
Yes, it's redundant. I wouldn't like to say it with the intention, but sometimes it could be inevitable.
Vして帰る is a common phrase to tell "do V and/then go back (home)", but it doesn't imply the V is conducted during the way back. 帰り for "way back home" or "going home" is also a commonly used word, but 帰りに買う doesn't necessarily mean it'll be brought home (or anything comes after; i.e. handed over at the station, perhaps?).
So, maybe the speaker uttered it visualizing the whole sequence they would drop into the store on the way back home, buy that thing, and bring it back home to eat.
From my experience, at work you often hear 「もう帰った」 for a situation when someone left work, but that does not mean someone has already reached his home. So the sentence could mean something like「仕事から帰る途中でパンを買って、家に帰ります」, but first 帰る and second 帰る would relate to different action.
If you left out the second 「帰ります」in your sentence it could simply state "I will buy (the bread) when coming back from work"
But with both 帰◯ in place I read it more like: "Today, after leaving work I will go to buy the bread and only then return home" (indicating the way back home will take more time than usual).
Yes, as you say, it's redundant. However, if you focus on how you return home, you will say it.
