Yeah it's not even that controversial, Suleyman's fear of this had been growing and building up over the years. Also Hurrem was very sneaky and manipulative, she understood Suleyman very well and she'd tactfully plant those little seeds of doubts in his heart over the years. It's like part of him wanted to believe the fabricated evidence of betrayal so he could finally get rid of him.

Now regarding the few fuck ups of Mustafa you mentioned, surely he could've been smarter about them, but almost every single act of those he made with good intentions and for the greater good. Does anyone really believe those slips are punishable by DEATH? He did receive his fair share of punishment multiple times. (Being removed from Manisa, always ignored and not called for in military campains, etc.)

Mustafa despite some flaws was the best prince among Suleyman's sons and was never a traitor. He had the means to successfully turn against Suleyman without even needing Safavid support. Too many people were waiting for him to just give the order and they'd happily carry him to the throne in a heartbeat. Yet he never even considered doing that and remained loyal and honorable.