The mood of Pilgrim's Progress is pious (or religious), dramatic, yearning, and triumphant.
The novel takes it for granted that readers are fully bought into and committed to its Protestant religious worldview, and the mood reinforces that perspective at every turn, with biblical allusions sprinkled throughout. The constant Bible quotation isn't simply didactic, but also a model for how Bunyan thinks Christians should believe and use the Bible in their everyday lives.
Subtlety of mood isn't a feature of the book, to put it mildly. Main characters regularly weep, pray aloud, sing, and laugh in response to the struggles and joys they face throughout their pilgrimages. They engage in tension-filled combat, conduct theological and ethical debates, and speak longingly of Heaven. This foregrounding of earnest, dramatic religious feeling is, once again, Bunyan's model for ordinary Christian piety. Readers obviously won't experience most of the specific events the characters do, but the overall peaks and valleys of their spiritual experience, Bunyan suggests, will be broadly the same.
Finally, the gleaming sights and joyful songs of the Celestial City, after so much wandering, privation, and doubt, ends both Parts 1 and 2 of the book with a mood of joyful triumph that's only been hinted at before. This climactic mood is meant to be readers' lasting takeaway, as Heaven should be their goal just as it is Christian's and Christiana's.