Short answers, pulled from the story.
Geoffrey of Monmouth published The History of the Kings of Britain in the 12th century. This text contains the first known written account of Cordelia as Queen.
The original Shakespeare text states that she is ultimately hanged. Her death marks the tragic conclusion of the narrative arc involving her family after being captured by Edmund's forces.
Nahum Tate published The History of King Lear in 1681 as an adaptation where Cordelia survives instead of being executed. She marries Edgar rather than remaining single or dead and becomes ruler of the kingdom alongside her husband.
Florence Pugh appeared in a 2018 Amazon production directed by Richard Eyre. This film features her portrayal of the character from the Shakespearian play.
Geoffrey of Monmouth described her reign and her eventual death in a historical context rather than a theatrical one. No other document before this text mentioned her name or deeds.