Pharaoh's hardened heart
Pharaoh hardens his own heart in some scenes (Exodus 8:15, 8:32) and Yahweh hardens it in others — divine sovereignty and human agency, read through Romans 9:17-18.
Exodus 9:12
12Yahweh hardened the heart of Pharaoh, and he didn’t listen to them, as Yahweh had spoken to Moses.
Exodus 8:15
15But when Pharaoh saw that there was a respite, he hardened his heart, and didn’t listen to them, as Yahweh had spoken.
What each tradition says
Rabbinic / Midrashic
Rabbi Yoḥanan said Exodus 10:1 gives heretics an opening to claim Pharaoh had no opportunity to repent. Rabbi Shimon ben Lakish answered that the Holy One blessed be He forewarns a person the first, second, and third time; if he does not relent, He locks his heart from repentance to exact retribution for his sins.
Shemot Rabbah (Exodus Rabbah; anonymous midrash, reported speech of Rabbi Yoḥanan and Resh Lakish); English: The Sefaria Midrash Rabbah, 2022, Shemot Rabbah (Exodus Rabbah) — Shemot Rabbah 13:3, on Exodus 10:1 ('I have hardened his heart')
Patristic
Augustine states that God hardened Pharaoh by His just judgment. Pharaoh also hardened himself by his own free will.
Augustine of Hippo (354-430), A Treatise on Grace and Free Will (trans. Peter Holmes and Robert Ernest Wallis), in NPNF ser. 1, vol. 5: St. Augustin: Anti-Pelagian Writings (ed. Philip Schaff, 1887) — Chapter 45 [XXIII], on Romans 9:18 and Exodus 8:32
Catholic
Aquinas distinguishes two things in spiritual blindness and hardness of heart. As the mind cleaves to evil and turns from the Divine light, God is not their cause, just as He is not the cause of sin. But as withdrawal of grace, leaving the mind unenlightened and the heart unsoftened, God is their cause.
Thomas Aquinas (1225-1274), Summa Theologiae, Second and Revised Edition (trans. the Fathers of the English Dominican Province; New Advent online) — I-II, q. 79, art. 3 ('Whether God is the cause of spiritual blindness and hardness of heart')
Orthodox
Chrysostom says Pharaoh was a vessel of wrath: by his own hard-heartedness he had kindled the wrath of God. After enjoying much long-suffering, Pharaoh became no better but remained unimproved.
John Chrysostom (c. 349-407), Homilies on the Epistle to the Romans, Homily XVI (trans. J. B. Morris, rev. W. H. Simcox; Oxford 1876), in NPNF ser. 1, vol. 11 (ed. Philip Schaff, 1889) — Homily XVI, on Romans 9:21-23 (the vessel of wrath fitted for destruction)
Reformed / Protestant
Calvin says Pharaoh, when deprived of others' assistance and abandoned, was neither changed nor softened, proving he was not so much deceived by their impostures as stupefied by his own malice and perversity. Yet Moses repeats that God hardened his heart, because God desired an occasion to manifest His power, as if by an opposing barrier.
John Calvin (1509-1564), Commentaries on the Four Last Books of Moses, Arranged in the Form of a Harmony, vol. 1 (trans. Charles William Bingham, Calvin Translation Society, 1852) — Commentary on Exodus 9:12 (section 'Exodus 9:8-12')
Evangelical
Wesley says the Lord hardened Pharaoh’s heart after Pharaoh had already hardened his own heart and resisted God’s grace. God then justly gave him up to his own heart’s lusts and strong delusions, permitting Satan to blind and harden him. Wilful hardness is commonly punished with judicial hardness.
John Wesley (1703-1791), Explanatory Notes upon the Old Testament (1765; CCEL's 'Wesley's Notes on the Bible') — Note on Exodus 9:12