I have found this article by G.K. Beale to be a really helpful resource in understanding the hardening of Pharaoh's heart. It is technical, but you can skip the parts in Hebrew and still get the gist of things. If you are trying to carefully think through the first cause of hardening (was it Pharaoh or God or both?) then this is a must read. I am grateful you can read it for free!
Here is a sample:
"A classic and important objection to this idea is that it associates God too closely with the cause of sin. No doubt the theologian must be very careful in discussing God's relation to sin. Nevertheless, the above exegesis shows that Exod 4-14 says that God was the ultimate, unconditional cause of Pharaoh's volition while holding him accountable for his disobedient volitional acts. While many theologians see an antinomy between divine sovereignty and human freedom in Exod 4-14 and Rom 9, the present evidence places the mystery between divine sovereignty and human accountability."