This confuses me a bit Djoperdjo, because to me the entire concept of trusting is
not having to have this conversation speaking about each other's intentions. Shadowheart says "Her fate is mine to seal. Let me handle this" and I'm trusting her to make the right decision in handling this situation based on the foundation of trust I've built with her over act 1 and 2 leading up to this moment. To me, you are not talking about trust, you are talking about convincing and asking permission. Having the spear yourself instead of her having it in the first place is already strange in this scenario, because it's her spear to get. Upon going to that library section to go get that spear, you've agreed to accompany her as she grabs it, so she already has the spear anyways at that point.
"I will spare Aylin if you want it so much - just give me the spear and let me approach her"
To me, this isn't trusting, this is her having to convince you that she can be trusted. And it implies that right before she says this, you have actually told her that you didn't trust her or expressed doubt about being able to trust her, which is why she's trying to convince you that she can be trusted. So to me, the starting point of this conversation would be the opposite of trust. In my case, Shadowheart has already earned my trust leading up to this scenario and I don't need another conversation to reaffirm this trust. If she didn't have my trust after clearing out act 1 and most of act 2, I probably would have gone behind her back and would have entered Shar's temple without her all together.
And naming the kind of trust currently available to you in the game at that moment as servility instead is interesting to me considering the start of this topic. To me, the way you have described how you'd want Lae'zel and Shadowheart to reply to your decisions in the game once you have reached 100% approval with them is that they show servility to you. I'd see true friends as being a two-way street of knowing each other, understanding each other, trusting each other and not expecting the other to go against their core beliefs and ultimate life goals on a whim when you say so.
Lae'zel is annoyed if you didn't go the direct route in accepting Raphael's deal to get the Orphic Hammer, but she trusts you in the moment. Later when you explain your intent to go the House of Hope to steal it from Raphael, a far more perilous path to acquire it, she even ends up saying she admires you for choosing this path. That's a true friend to me.
However, then later expecting Lae'zel to give up any hope for her people to fight against Vlaakith's oppression by choosing the Emperor, a mindflayer, over Orpheus, that is not something a true friend would ever ask of her. Her not being accepting of this choice makes total sense, you've betrayed her in this moment and have broken her trust in you. If she would go along with this just because you want it, then she's not a true friend, she'd be servile to you in that case. Overall your concept of what a true friend is to you comes across as very much of a one-way street. You seem to want to be able to disregard their wants and needs and expect to be able to ignore your part of being a true friend to them, then expect them to be servile to you if you do something that goes against their wishes and goals.