Luke and Leia never sensed that they were twins until Return of the Jedi despite both being sensitive to the Force. Anakin Skywalker's twin children are the original Star Wars trilogy's driving force, having been separated after Padme's death. After the shocking revelation that Darth Vader is his father, Luke also discovers that he has a sister. Although Luke and Leia are both quick to figure out their connection in Return of the Jedi, it seems odd that they didn't realize they were twins sooner.
Luke Skywalker and Leia Organa are born at the end of Revenge of the Sith. The twins are quickly hidden from Anakin and each other in order to protect them. Years later, Darth Vader is astute enough in the Force that he not only senses Obi-Wan's presence in A New Hope but also identifies Luke Skywalker as his son in The Empire Strikes Back's earth-shattering conclusion. After this revelation, Luke connects the dots to realize that Leia is his sister, finally telling her in Return of the Jedi before leaving to face Vader one last time. From this point, Luke and Leia's connection becomes stronger, as does their oneness with the Force, as demonstrated in The Last Jedi through Leia's space travel and Luke's projection trick against Kylo Ren.
There are clues in Star Wars to suggest that Luke and Leia did, in fact, know vaguely about their relation to each other much earlier than Return of the Jedi, but perhaps, were not yet Force-sensitive enough to have the full picture. One clue comes in The Empire Strikes Back when Luke is clinging for his life. Luke cries out for Leia in desperation and Leia senses him, convincing Lando to take the Millennium Falcon back to Luke's precise location and rescue him. When Luke tells Leia that they are twins she also responds casually "I know. I've always known." This is slightly jarring given their passionate kiss in The Empire Strikes Back, but Leia's lack of surprise could be speaking in retrospect; she's always felt a strong draw to Luke that scales the depths of a sibling's love.
How Star Wars: Visions' Twins Compare To Luke and Leia
Star Wars: Visions has an episode called The Twins where two Force-sensitive twins, Am and Karre fight over a powerful kyber crystal. Although Am and Karre are both Sith, Karre dissents after having a vision of his sister's death at the hands of the overpowered crystal. The twins can fully sense one another, often anticipating each other's moves, with Karre even sensing that Am is alive after an explosive conclusion. These twins appear to be more connected than Luke and Leia were, but Am explains that she and Karre were created by Sith alchemy, specifically created and training together to serve the dark side of the Force. Although they are still biological twins, they have been created and trained with purpose in a way that Luke and Leia never were.
Luke and Leia's connection in the Force exponentially grows after they learn about their relationship in Return of the Jedi. As Luke and Leia both become more aware of the Force, they are able to more intentionally use it, thus also allowing them to tap into a greater connection with one another in later Star Wars adventures. Whereas Am and Karre in Star Wars: Visions were created intentionally to be always connected, Luke and Leia discover the depths of their connection in Return of the Jedi and that the Force has been guiding them all along. This ultimately makes for a more powerful story than had Luke and Leia sensed each other fully from the beginning.