Snape's unbreakable pledge in Harry Potter and the Half-Blood Prince was given a deeper meaning in Fantastic Beasts: The Secrets of Dumbledore.
The blood contract Geller Grindelwald and Albus Dumbledore shared as children is explored in Fantastic Beasts: The Secrets of Dumbledore, which adds tragic intricacy to Professor Snape's unbreakable pledge in Harry Potter and the Half-Blood Prince. Unbreakable bonds are a popular sort of magic in the Harry Potter universe, and Dumbledore's experience with binding charms in Fantastic Beasts 3 lends credence to the idea that he can empathise to Snape.
Severus Snape (Alan Rickman) makes an unbreakable vow with Draco Malfoy's mother, Narcissa Malfoy (played by Helen McCrory of Peaky Blinders), in Harry Potter and the Half-Blood Prince, in which he promises to protect Draco until the boy kills Dumbledore, but will kill Dumbledore himself if he fails. Dumbledore knows this because he wants Snape to kill him in order to gain Voldemort's trust and pull off a double-cross. Draco is unable to kill Dumbledore, thus in the final act of Harry Potter and the Half-Blood Prince, Snape honours the vow's contract by doing as he is told.
A Harry Potter Snape Spell Theory is Disproven in Fantastic Beasts 3.
Because the blood contract that he and Grindelwald (Mads Mikkelsen) forged together is purportedly forever binding, Dumbledore (Jude Law) was familiar with unbreakable vows at the time, as shown by the Fantastic Beasts films. They were young when they tied themselves together because they were in love. Years later, when Dumbledore needs to defeat him, the pact poses issues because the charm prevents them from harming one other unless the pact is broken. When Dumbledore and Snape plot to assassinate Voldemort, the former's faith in and affection for the latter is explained by his experiences with Grindelwald and his understanding of the inevitability of a magical link. Snape understands that if he makes the unbreakable vow, he will be unable to back out of killing Dumbledore without dying.
Snape, like everyone else in Dumbledore's army, wants to fight for good, and by working as a plant in Voldemort's forces, he risks his emotional comfort and the trust of other comrades (for example, Minerva McGonagall). He also can't change his mind about killing Dumbledore, something Dumbledore must have felt strongly about given the terrible irreversibility of his own blood covenant with Grindelwald. This link elaborates on Dumbledore's unfettered faith in Snape's devotion, which is only touched upon briefly in Harry Potter and the Deathly Hallows — Part 2.
The blood charm that Dumbledore wears in Fantastic Beasts 3 fractures by the end of the film, allowing him and Grindelwald to fight one other. Although the charm does not have the same magical properties as an unbreakable vow, the effect is comparable. Furthermore, even when Dumbledore is offered a definite chance to confront Grindelwald, he is unable to prevail. Despite the charm breaking, there is an undeniable affection between him and Grindelwald that demonstrates their link is as strong as it has always been. So it'd be hard for Dumbledore not to recognise what Snape is giving up by promising to Narcissa on a personal and empathic level.
The bargain Dumbledore made with Grindelwald when he was younger, as revealed in Fantastic Beasts: The Secrets of Dumbledore, strengthens his link with Snape. His devotion to Grindelwald is as unbreakable as Snape's promise to assassinate Dumbledore, making their relationship in the last Harry Potter films all the more heartbreaking. Snape and Dumbledore's friendship will remain one of the most important aspects of the franchise, especially now that Dumbledore's backstory has been revealed.