Is Hamlet a revenge play?

Hamlet has many of the elements of the Elizabethan revenge drama or tragedy, but it is also a psychological drama in two significant ways. Young Hamlet does finally avenge the death of his father, also Hamlet, by killing his murderer, Claudius. Along the way, however, he accidentally kills Polonius, so Laertes must avenge his father’s death; he also does this at the play’s end by killing Hamlet. The second revenge plot largely serves to support the main one by emphasizing the motif of father-son bonds. However, although a lot of people die in the play, only a few of those killings are actually acts of revenge, which is different from the typical Elizabethan version.
Many people have argued that the differences from the genre account for this play’s longevity. Hamlet’s psyche is really the subject, as his conscience and indecisiveness block him for a long time from taking the act of vengeance. The psychological aspects also include suspense similar to a modern detective story. If the audience believes the Ghost right away, then Claudius is certainly guilty. Until Claudius admits his guilt, the audience cannot be sure if Hamlet is right to be so cautious.
https://www.britannica.com/art/revenge-tragedy

Shakespeare's Hamlet is considered a "revenge play." Quite specifically, the ghost asks Hamlet to "revenge his foul and most unnatural murder." The ghost, of course, indicates who the murderer is: "But know, thou noble youth, / the serpent that did sting thy father's life / Now wears his crown." Here we should also note that the ghost certainly does not extend this revenge to Hamlet's mother, the queen. We know this because the ghost warns in his monologue: "But howsoever thou pursues this act, / Taint not thy mind, nor let thy soul contrive / Against thy mother aught. Leave her to heaven / And to those thorns that in her bosom lodge to prick and sting her." As the ghost admits, Queen Gertrude will beat herself up enough with guilt. How does this introduction as a revenge play compare with others of its time? Well, as was important to all Elizabethans, the divine order of things must (above all else) be preserved. In this case (as in may other revenge plays), a corruption of this order appears in the killing of a king. The order must be set right through revenge. Hamlet, then, fits quite nicely within the revenge play genre.