I note that your question says that:
What are several different ways to incorporate true facts into
historical fiction without just giving a massive info dump?
So you want to set your story or stories in historical times and places. I note that the Historum site says that history ends and current events begin 30 years ago. And other websites and historical magazines may have different cut-off dates for history.
And on the other hand, recorded history began about 5,000 years ago about 3000 BC when then-current events like the names of kings began to be recorded.
And every place in the world today now has a written recorded history going back for decades, and usually for centuries, and often for millennia. And many of the places where history began to be recorded the most recently have oral history of varying degrees of accuracy going back generations or centuries more.
So the settings of historical fiction can include times and places where there a vast range in the amount and accuracy of history available to average persons, or to especially ignorant persons, or to especially well-educated persons, or whatever type of persons your characters may be.
So how the characters learn historical facts, legends, and myths can vary greatly between various historical periods and various persons within the same period.
Have you ever heard about the Schleswig-Holstein question, which was important in the 19th century and was the cause of the First Schleswig War and the Second Schleswig War in 1848-1851 and 1864?
The Schleswig-Holstein question involved a lot of complex history, so complex as to inspire a famous joke:
The British statesman Lord Palmerston is reported to have said: "Only three people have ever really understood the Schleswig-Holstein business—the Prince Consort, who is dead—a German professor, who has gone mad—and I, who have forgotten all about it."1
And obviously, if historical fiction is set during the period of the Schleswig-Holstein question, or one of the two Schleswig Wars, the characters on one side might ask what it is all about and be told their side's versions, which the naive may accept and the cynical express skepticism about.
And maybe someone will ask about how the other side justifies their obviously wrong stance and may be given a version of their claims.
Or the story could be set in a divided community where members of different sides proclaim their views at the drop of a hat.
When King Alexander III of Scotland died in 1286, his little granddaughter Margaret The Maid of Norway was recognized as the rightful queen. But Margaret died in the Orkney Islands when sailing to Scotland in 1290, and nobody else was closely related to King Alexander III. The process of finding an heir is known as "the Competition for the crown of Scotland" or "the Great Cause".
Eleven Scottish & English nobles, one noble from the Holy Roman Empire, and a foreign king made hereditary claims with various degrees of validity to the throne.
So obviously any story set in Scotland at that time could include a lot of
discussions of genealogy and succession rules as people argued about who the best heir was. Some people might propose that someone with a poor claim should be the rightful king, and then someone else might say they are only claiming that because they are closely related to that candidate and thus possibly could inherit the throne if their candidate wins, and thus mentioning more noble genealogy.
And of course, there have been many other succession disputes in history, though most were less complicated than this one.
I can imagine that during the Wars of the Roses period, for example, some kids might wonder about the claim of Richard Duke of York (1415-1460) to the throne of England. One may say they heard Richard was a grandson of King Edward III, another that he was a great-grandson, and another a great-great-grandson, and someone older might explain that Richard was the great-grandson of King Edward III on his father's side, and since his grandfather was a younger brother to the grandfather of King Henry VI, Richard was behind Henry VI in agnatic (male-only succession). But they might go onto say that Duke Richard was also a great-great-great-grandson of King Edward III through his mother Anne Mortimer, and she was descended from an even older son of King Edward III, thus giving Richard a superior claim to the crown if it can pass through females.
And of course, rather ordinary and non-royal families can have complicated family trees that someone has trouble keeping straight and needs to have explained to them.
For example, my great great great grandfather, Jabob Demuth (1779-1842), of Lancaster, PA, married three times. His first wife was a daughter of John Eberman by John Eberman's first wife, and they had a son Emmanuel Eberman Demuth (b. 1804) who has many descendants today. But John Emberman married and had children with a second wife who was a sister of Jacob Demuth. And in some times and places it was considered as wrong to marry someone related to you by marriage as someone related to you by blood - but obviously not in Lancaster PA, at that time.
John Eberman and his first wife had a son William Eberman, who married and had children with three wives. His first two wives were sisters and Demuth descendants. So William Eberman's children by his first two wives were both half-siblings and first cousins.
Jacob's Demuth's 2nd wife was, if I have interpreted the marriage record correctly, his niece, his brother's illegitimate daughter, and only 14 years younger than that brother. They had ten children, and at least one of them probably had descendants today.
A great great great great grandfather of mine, Henry Hurst (b. 1771) Gwynedd, PA, married Eva Lowman and had a daughters Anne Frances Veronica Hurst, born 1801. He moved to Lancaster, PA, and married a niece of Jacob Demuth in 1822, and had children, including Elam D. Hurst. And a few days later in 1822, Jacob Demuth married Ann Frances Veronica Hurst, who was his niece's stepdaughter and had nine children, including my ancestor.
So the nine children of Jacob Demuth and Ann Frances Veronica Hurst were the first cousins of Elam D. Hurst's mother, and they were also Elam D. Hurst's half nephews and nieces, the children of his half-sister. Henry Hurst was both Jabob Demuth's father-in-law and nephew-in-law.
So I can imagine that some kids in those families could be confused about their relationships, and an older relative might draw them a family tree to help explain it to them. Or someone might picture a family tree in their mind to figure out relationships in their extended family. And such family trees can be included as illustrations in a work of historical fiction.
And I am sure that has happened countless times in real life, often to explain relationships that are much less complicated, and so it can also happen in fiction.
Or some Roman could hear that their great great grandfather fought in the war with Carthage and say they thought that their grandfather did. And they could be told there were two wars with Carthage and grandfather fought in the second and great-great-grandfather in the first.
Or someone could be confused about which side Japan and Italy fought on during the World Wars, and someone could tell them that both countries fought against Germany during World War One and both were allied to Germany in World War two, although Italy switched sides in 1943.
Since a lot of historical information is rather confusing, it is only natural that some characters in a work of historical fiction could be confused, perhaps having heard contradictory claims, about the historical background to current events, and ask someone for more information. And that person could answer their questions and clear up their confusion and give them an accurate account - at least as accurate as that other person understands it.