As others have said, there isn’t much story for most of the game outside of subtle, environmental story that can only be inferred. The biggest story beats happen at the very beginning and very end of the game.

Those callbacks that are annoying rehashes for you are intended to be nostalgic for players of the first game. Keep in mind that there was an 8 year gap between console metroid games.

If you aren’t having fun playing the game, then it’s failing at its primary goal. Feel free to skip the rest of the game, but please be sure to at least watch an online video of the ending, before, during, and after the final boss. The opening of Fusion and other future games in the series reference that ending, and it’s absolutely an iconic piece of gaming history.