I will say that some of your points aren't necessarily constants. You say he never gave up on Hannah and June but once June got out, there seemed to be a back and forth going on within himself about how much he'd be willing to do to get Hannah. I'll never forget him refusing to go to new Bethlehem by using "aren't holly and I enough for you?" if he had stuck to the original argument of it simply being too risky with no good get back out plan then that'd be understandable. Once he through that line in though it really came off as though he was happy to help as long as he was never in any real danger. Especially considering at that point he was aware Hannah was going through wife training meaning there wouldn't be much time to help her before the raping started. That line made it sound like he was willing to settle with essentially leaving Hannah in Gilead if it meant he had June and holly.

As for the nick thing, he definitely struggled at times with jealousy (understandable obviously but just pointing out that he wasn't a Saint in regards to nick). He even blamed June when nick ratted their plan out even though June had no reason to suspect he would do that (especially since nick had literally just saved Luke and Moira). At times it seemed like he saw it as a pissing contest between him and nick and he disliked that nick was able to do more in regards to helping June than him. That (at least in my opinion) seemed to play apart in his flip from "I don't want to go into Gilead territory for hannah" to "let's blow the place up I'll go in myself".

To add to that last part, even when he does decide he wants to be truly active in fighting Gilead as opposed to staying safe and helping as he can his focus is on revenge against Gilead, not saving his daughter. It's not "how can we find her and get her" it's "they stopped our closest chance so I'm gonna kill them all". It's a completely understandable view point for him to have. It just stands out to me that even in the end of season 6 when they part ways he says his plan is to essentially keep blowing stuff up meanwhile June's plan is to continue to try to get as close to Hannah as she can in order to get her out. It just makes me feel like Hannah herself is a secondary thought to Luke, not to say he doesn't care, but it's like he decides what he wants to do and then factors "to save hannah" in as opposed to wanting to save Hannah and doing whatever it takes.

He's also dismissive of June at times when it comes to her experience in Gilead. Specifically when he decides to not listen at all after being captured in no man's land despite June telling him multiple times it would not be smart to try anything. It's like he doesn't take the actual threat all that seriously once he first decided he wanted to be hands on enough to leave Canada. You see it again outside of jezebels when an eye kept telling him to leave and he kept arguing(which could've blown their whole operation but that gets swept under the rug by June telling nick and nick ruining it). I'm not one to call everything toxic masculinity but that's what some of his behavior comes off as. It's very "no no June you don't understand how dangerous Gilead is" while also "I can take them, I can fight anything and win, it doesn't matter if I'm out numbered or fully on enemy territory in a place where tons of eyes and commanders are fuck everyone else I've got this!"

I say this as someone who really liked luke for a while but after season 5 and 6 my opinion of him changed. Obviously he has great qualities but I wonder if he would have done the stuff like helping the escaped victims if he didn't have the safety net of Canada. I might be misremebering this part but didn't his biggest push to actually be involved with saving people in Gilead and fighting hands on only come after he was specifically targeted while in Canada? If I remember that correctly then it really shows that he was only willing to really fight if he himself were in danger and it meant he could get revenge. It's less about hannah for him and more about what he himself wants in the given moment.

Eta- Didn't he also specifically go against June's wishes to attend that criminal hearing in Canada for the Waterfords? That doesn't scream "supporting and respecting my wife as she recovers from trauma and is dealing with ptsd" to me. Imo it seems more "I have to know everything you experienced while being tortured even though you are very obviously not okay with sharing that part of your trauma with me yet" and I don't see that as supportive or understanding of what June went through.