Which should be used in an English publication? Should the APA-LC be Pushkin or Pу́shkin?
That dash above the у́ is called "stress accent". Wikipedia marks stress accent in the names of its articles. Such stress accents are not written in most of the Russian texts, they are used mostly in encyclopedias, dictionaries, Russian textbooks ans sometimes in books for children. The stress on y means that it is this vowel sound which is the loudest and longest in the word, in Russian you pronounce Пушкин as POOSH-kin. Again, in usual texts those stress accents are not used. Note that later in the Russian Wikipedia article no stress accent is put. In English the standart spelling of that surname is